A101562 a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+4*x^k)}.

1, 3, 17, 67, 257, 1011, 4097, 16451, 65553, 261891, 1048577, 4195379, 16777217, 67104771, 268435729, 1073758275, 4294967297, 17179804659, 68719476737, 274878168899, 1099511631889, 4398045462531, 17592186044417, 70368748389427

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * 4^k * A051731(n+1, k+1).

a(n) = (-1)^n * Sum_{d|n+1} (-4)^(d-1). - G. C. Greubel, Jun 25 2024

Mathematica

A101562[n_]:= (-1)^n*DivisorSum[n+1, (-4)^(#-1) &];
Table[A101562[n], {n, 0, 40}] (* G. C. Greubel, Jun 25 2024 *)

Prog

(Magma)
A101562:= func< n | (&+[(-1)^(n-k)*4^k*0^((n+1) mod (k+1)): k in [0..n]]) >;
[A101562(n): n in [0..40]]; // G. C. Greubel, Jun 25 2024
(SageMath)
def A101562(n): return sum((-1)^(n+k)*4^k*0^((n+1)%(k+1)) for k in range(n+1))
[A101562(n) for n in range(41)] # G. C. Greubel, Jun 25 2024

Crossrefs

Cf. A048272, A051731, A081295, A101561, A101563.

Sequence in context: A227427 A120386 A061982 * A034566 A357923 A069468

Adjacent sequences: A101559 A101560 A101561 * A101563 A101564 A101565

Keyword

easy,nonn

Author

Paul Barry, Dec 07 2004

Status

approved