Sequences

392,541 sequences

a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (composite numbers).A024461
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (composite numbers).
Triangle T(n,k) read by rows, arising in enumeration of catafusenes.A024462
Triangle T(n,k) read by rows, arising in enumeration of catafusenes.
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (odd natural numbers).A024463
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (odd natural numbers).
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A000201 (lower Wythoff sequence).A024464
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A000201 (lower Wythoff sequence).
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = A001950 (upper Wythoff sequence).A024465
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), 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 = (Fibonacci numbers), t = A023533.A024466
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (Fibonacci numbers), 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 = (Fibonacci numbers), t = A014306.A024467
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), 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 = (Fibonacci numbers), t = (primes).A024468
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (primes).
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers).A024469
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (1, p(1), p(2), ...).A024470
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), 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 = (Lucas numbers), t = (composite numbers).A024471
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (composite numbers).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (F(2), F(3), ...).A024472
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (F(2), F(3), ...).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (odd natural numbers).A024473
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), 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 = (Lucas numbers), t = A000201 (lower Wythoff sequence).A024474
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A000201 (lower Wythoff sequence).
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A001950 (upper Wythoff sequence).A024475
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), 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 = (Lucas numbers), t = A023533.A024476
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = (Lucas numbers), t = A023533.
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A014306.A024477
s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), 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 = (Lucas numbers), t = (primes).A024478
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = (primes).
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (1, p(1), p(2), ...).A024479
a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (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 = (1, p(1), p(2), ...), t = (composite numbers).A024480
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (1, p(1), p(2), ...), t = (composite numbers).
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (1, p(1), p(2), ...), t = (F(2), F(3), ...).A024481
a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (1, p(1), p(2), ...), t = (F(2), F(3), ...).
a(n) = (1/2)*(binomial(2n, n) - binomial(2n-2, n-1)).A024482
a(n) = (1/2)*(binomial(2n, n) - binomial(2n-2, n-1)).
a(n) = binomial(2*n, n) mod binomial(2*n-2, n-1).A024483
a(n) = binomial(2*n, n) mod binomial(2*n-2, n-1).
Duplicate of A007226.A024484
Duplicate of A007226.
a(n) = (2/(3*n-1))*binomial(3*n,n).A024485
a(n) = (2/(3*n-1))*binomial(3*n,n).
a(n) = (1/(2n+1))*Multinomial(3n; n,n,n).A024486
a(n) = (1/(2n+1))*Multinomial(3n; n,n,n).
a(n) = (1/(4n+2))*M(3n; n,n,n).A024487
a(n) = (1/(4n+2))*M(3n; n,n,n).
a(n) = (1/(3n-1))*M(3n; n,n,n), where M(...) is a multinomial coefficient.A024488
a(n) = (1/(3n-1))*M(3n; n,n,n), where M(...) is a multinomial coefficient.
a(n) = (1/(9n-3))*M(3n; n,n,n), where M() is a multinomial coefficient.A024489
a(n) = (1/(9n-3))*M(3n; n,n,n), where M() is a multinomial coefficient.
a(n) = C(n-1,1) + C(n-3,3) + ... + C(n-2*m-1,2*m+1), where m = floor((n-2)/4).A024490
a(n) = C(n-1,1) + C(n-3,3) + ... + C(n-2*m-1,2*m+1), where m = floor((n-2)/4).
a(n) = (1/(4n-1))*C(4n,2n).A024491
a(n) = (1/(4n-1))*C(4n,2n).
Catalan numbers with odd index: a(n) = binomial(4*n+2, 2*n+1)/(2*n+2).A024492
Catalan numbers with odd index: a(n) = binomial(4*n+2, 2*n+1)/(2*n+2).
a(n) = C(n,0) + C(n,3) + ... + C(n,3[n/3]).A024493
a(n) = C(n,0) + C(n,3) + ... + C(n,3[n/3]).
a(n) = C(n,1) + C(n,4) + ... + C(n, 3*floor(n/3) + 1).A024494
a(n) = C(n,1) + C(n,4) + ... + C(n, 3*floor(n/3) + 1).
a(n) = C(n,2) + C(n,5) + ... + C(n, 3*floor(n/3)+2).A024495
a(n) = C(n,2) + C(n,5) + ... + C(n, 3*floor(n/3)+2).
a(n) = (3/(8n-4))*C(4n,n).A024496
a(n) = (3/(8n-4))*C(4n,n).
Duplicate of A007228.A024497
Duplicate of A007228.
a(n) = [ C(2n,n)/n ].A024498
a(n) = [ C(2n,n)/n ].
a(n) = [ C(2n,n)/(n-1) ].A024499
a(n) = [ C(2n,n)/(n-1) ].
a(n) = [ C(2n,n)/n^2 ].A024500
a(n) = [ C(2n,n)/n^2 ].
a(n) = floor(C(4n,2n)/C(4n,n)).A024501
a(n) = floor(C(4n,2n)/C(4n,n)).
a(n) = floor(C(2n,n)/2^n).A024502
a(n) = floor(C(2n,n)/2^n).
a(n) = floor(binomial(2*n,n)/3^n).A024503
a(n) = floor(binomial(2*n,n)/3^n).
a(n) = floor(C(2n,n)/2^(n+1)).A024504
a(n) = floor(C(2n,n)/2^(n+1)).
a(n) = [ C(2n,n)/2^(n+2) ].A024505
a(n) = [ C(2n,n)/2^(n+2) ].
a(n) = [ C(2n,n)/2^(n+3) ].A024506
a(n) = [ C(2n,n)/2^(n+3) ].
Numbers that are the sum of 2 distinct nonzero squares (with repetition).A024507
Numbers that are the sum of 2 distinct nonzero squares (with repetition).
Numbers that are a sum of 2 distinct nonzero squares in more than one way.A024508
Numbers that are a sum of 2 distinct nonzero squares in more than one way.
Numbers that are the sum of 2 nonzero squares, including repetitions.A024509
Numbers that are the sum of 2 nonzero squares, including repetitions.
Positions of even numbers in A004431 (sums of 2 distinct nonzero squares).A024510
Positions of even numbers in A004431 (sums of 2 distinct nonzero squares).