Sequences

392,541 sequences

Catacondensed simply-connected monopentapolyhexes.A024311
Catacondensed simply-connected monopentapolyhexes.
a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3).A024312
a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3), t = A023531.A024313
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3), t = A023531.
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3), t = A023532.A024314
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (natural numbers >= 3), t = A023532.
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = floor(n/2), s = (natural numbers >= 3), t = (Fibonacci numbers).A024315
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = floor(n/2), s = (natural numbers >= 3), t = (Fibonacci numbers).
a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = A023531.A024316
a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = A023531.
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A023532.A024317
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A023532.
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Fibonacci numbers).A024318
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Fibonacci numbers).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Lucas numbers).A024319
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (Lucas numbers).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (1, p(1), p(2), ... ).A024320
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, 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 = floor((n+1)/2), s = A023531, t = (composite numbers).A024321
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (composite numbers).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (F(2), F(3), ...).A024322
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (F(2), F(3), ...).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (odd natural numbers).A024323
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (odd natural numbers).
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A000201 (lower Wythoff sequence).A024324
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A000201 (lower 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 = A023531, t = A001950 (upper Wythoff sequence).A024325
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, 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 = A023531, t = A023533.A024326
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A023533.
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor( (n+1)/2 ), s = A023531, t = A014306.A024327
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor( (n+1)/2 ), s = A023531, t = A014306.
a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).A024328
a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*prime(n-j+1).
Expansion of log(1+log(1+x)^2)/2.A024329
Expansion of log(1+log(1+x)^2)/2.
Expansion of tanh(log(1+x))*log(1+x)/2.A024330
Expansion of tanh(log(1+x))*log(1+x)/2.
Expansion of log(1+x)*log(1+tanh(x))/2.A024331
Expansion of log(1+x)*log(1+tanh(x))/2.
E.g.f.: sin(log(1+x))*log(1+x)/2.A024332
E.g.f.: sin(log(1+x))*log(1+x)/2.
Expansion of e.g.f: tanh(log(1+x)^2)/2.A024333
Expansion of e.g.f: tanh(log(1+x)^2)/2.
Expansion of sin(log(1+x)^2)/2.A024334
Expansion of sin(log(1+x)^2)/2.
Expansion of sinh(log(1+x)^2)/2.A024335
Expansion of sinh(log(1+x)^2)/2.
Expansion of e.g.f.: tan(log(1+x)^2)/2.A024336
Expansion of e.g.f.: tan(log(1+x)^2)/2.
Expansion of sinh(log(1+x))*log(1+x)/2.A024337
Expansion of sinh(log(1+x))*log(1+x)/2.
Expansion of log(1+x)*log(1+tan(x))/2.A024338
Expansion of log(1+x)*log(1+tan(x))/2.
Expansion of tan(log(1+x))*log(1+x)/2.A024339
Expansion of tan(log(1+x))*log(1+x)/2.
Duplicate of A012667.A024340
Duplicate of A012667.
Duplicate of A012528.A024341
Duplicate of A012528.
Expansion of e.g.f. tanh(x)*tan(x), coefficients of powers x^(4*n+2).A024342
Expansion of e.g.f. tanh(x)*tan(x), coefficients of powers x^(4*n+2).
Expansion of e.g.f. sin(x^2) in powers of x^(4*n + 2).A024343
Expansion of e.g.f. sin(x^2) in powers of x^(4*n + 2).
Duplicate of A012673.A024344
Duplicate of A012673.
Duplicate of A012524.A024345
Duplicate of A012524.
Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)).A024346
Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)).
Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)).A024347
Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)).
Expansion of tan(x^2).A024348
Expansion of tan(x^2).
Duplicate of A012529.A024349
Duplicate of A012529.
Duplicate of A012669.A024350
Duplicate of A012669.
Primes forming a 3 X 3 magic square with prime entries and minimal constant 177 = A164843(3).A024351
Primes forming a 3 X 3 magic square with prime entries and minimal constant 177 = A164843(3).
Numbers which are the difference of two positive squares, c^2 - b^2 with 1 <= b < c.A024352
Numbers which are the difference of two positive squares, c^2 - b^2 with 1 <= b < c.
Duplicate of A020883.A024353
Duplicate of A020883.
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of B, sorted and duplicates removed (first differs from A020883 at 420).A024354
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of B, sorted and duplicates removed (first differs from A020883 at 420).
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of AUB, sorted.A024355
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of AUB, sorted.
Determinant of Hankel matrix of the first 2n-1 prime numbers.A024356
Determinant of Hankel matrix of the first 2n-1 prime numbers.
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of AUBUC, sorted.A024357
Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives values of AUBUC, sorted.
Sum of the sizes of binary subtrees of the perfect binary tree of height n.A024358
Sum of the sizes of binary subtrees of the perfect binary tree of height n.
Number of primitive Pythagorean triangles with short leg n.A024359
Number of primitive Pythagorean triangles with short leg n.
Number of primitive Pythagorean triangles with long leg n.A024360
Number of primitive Pythagorean triangles with long leg n.