Sequences

392,541 sequences

Number of primitive Pythagorean triangles with leg n.A024361
Number of primitive Pythagorean triangles with leg n.
Number of primitive Pythagorean triangles with hypotenuse n.A024362
Number of primitive Pythagorean triangles with hypotenuse n.
Number of primitive Pythagorean triangles with side n.A024363
Number of primitive Pythagorean triangles with side n.
Ordered perimeters of primitive Pythagorean triangles.A024364
Ordered perimeters of primitive Pythagorean triangles.
Areas of right triangles with coprime integer sides.A024365
Areas of right triangles with coprime integer sides.
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = A023532.A024366
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = A023532.
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (Fibonacci numbers).A024367
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (Fibonacci numbers).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (Lucas numbers).A024368
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (Lucas numbers).
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (1, p(1), p(2), ...).A024369
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (1, p(1), p(2), ...).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (composite numbers).A024370
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (composite numbers).
Sum_{ k=1 ... floor(n/2) } A023532(k)*Fib(n-k).A024371
Sum_{ k=1 ... floor(n/2) } A023532(k)*Fib(n-k).
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (odd natural numbers).A024372
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (odd natural numbers).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A000201 (lower Wythoff sequence).A024373
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A000201 (lower Wythoff sequence).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A001950 (upper Wythoff sequence).A024374
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A001950 (upper Wythoff sequence).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023532, t = A023533.A024375
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023532, t = A023533.
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A014306.A024376
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A014306.
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (primes).A024377
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = (primes).
a(n) = 2nd elementary symmetric function of the first n+1 positive integers congruent to 1 mod 4.A024378
a(n) = 2nd elementary symmetric function of the first n+1 positive integers congruent to 1 mod 4.
a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 1 mod 4.A024379
a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 1 mod 4.
4th elementary symmetric function of the first n+3 positive integers congruent to 1 mod 4.A024380
4th elementary symmetric function of the first n+3 positive integers congruent to 1 mod 4.
a(n) = sum of squares of first n positive integers congruent to 1 mod 4.A024381
a(n) = sum of squares of first n positive integers congruent to 1 mod 4.
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 1 mod 4.A024382
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 1 mod 4.
a(n) = s(1)*s(2)*...*s(n)*(1/s(1) - 1/s(2) + ... + c/s(n)), where c = (-1)^(n+1) and s(k) = 4*k - 3 for k = 1, 2, 3, ....A024383
a(n) = s(1)*s(2)*...*s(n)*(1/s(1) - 1/s(2) + ... + c/s(n)), where c = (-1)^(n+1) and s(k) = 4*k - 3 for k = 1, 2, 3, ....
a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 4k-3 for k = 1,2,3,...A024384
a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 4k-3 for k = 1,2,3,...
a(n) = [ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 positive integers congruent to 1 mod 4}.A024385
a(n) = [ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 positive integers congruent to 1 mod 4}.
[ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.A024386
[ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.A024387
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.
[ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.A024388
[ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.A024389
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.
[ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.A024390
[ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.
2nd elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.A024391
2nd elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.
a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 2 mod 3.A024392
a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 2 mod 3.
4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3.A024393
4th elementary symmetric function of the first n+3 positive integers congruent to 2 mod 3.
a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3.A024394
a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3.
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.A024395
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.
a(n) = ( Product {k = 1..n} 3*k - 1 ) * ( Sum {k = 1..n} (-1)^(k+1)/(3*k - 1) ).A024396
a(n) = ( Product {k = 1..n} 3*k - 1 ) * ( Sum {k = 1..n} (-1)^(k+1)/(3*k - 1) ).
a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 3k-1 for k = 1,2,3,...A024397
a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 3k-1 for k = 1,2,3,...
a(n) = [ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 positive integers congruent to 2 mod 3}.A024398
a(n) = [ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 positive integers congruent to 2 mod 3}.
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.A024399
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.A024400
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.
a(n) = [ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.A024401
a(n) = [ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.A024402
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.
[ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.A024403
[ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.
Number of products of distinct primes <= prime(n) equal to -1 (mod prime(n)).A024404
Number of products of distinct primes <= prime(n) equal to -1 (mod prime(n)).
Number of products of distinct primes <= p(n) equal to 1 (mod p(n)).A024405
Number of products of distinct primes <= p(n) equal to 1 (mod p(n)).
Ordered areas of primitive Pythagorean triangles.A024406
Ordered areas of primitive Pythagorean triangles.
Areas of more than one primitive Pythagorean triangle.A024407
Areas of more than one primitive Pythagorean triangle.
Perimeters of more than one primitive Pythagorean triangle.A024408
Perimeters of more than one primitive Pythagorean triangle.
Hypotenuses of more than one primitive Pythagorean triangle.A024409
Hypotenuses of more than one primitive Pythagorean triangle.
Long leg of more than one primitive Pythagorean triangle.A024410
Long leg of more than one primitive Pythagorean triangle.