A101563 a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+10*x^k).

1, 9, 101, 1009, 10001, 99909, 1000001, 10001009, 100000101, 999990009, 10000000001, 100000100909, 1000000000001, 9999999000009, 100000000010101, 1000000010001009, 10000000000000001, 99999999900099909

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..990

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (10)^k * A051731(n+1, k+1).

a(n) = (-1)^n * Sum_{d|n+1} (-10)^(d-1). - G. C. Greubel, Jun 25 2024

Mathematica

A101563[n_]:= (-1)^n*DivisorSum[n+1, (-10)^(#-1) &];
Table[A101563[n], {n, 0, 40}] (* G. C. Greubel, Jun 25 2024 *)

Prog

(Magma)
A101563:= func< n | (&+[(-1)^(n-k)*(10)^k*0^((n+1) mod (k+1)): k in [0..n]]) >;
[A101563(n): n in [0..40]]; // G. C. Greubel, Jun 25 2024
(SageMath)
def A101563(n): return sum((-1)^(n+k)*(10)^k*0^((n+1)%(k+1)) for k in range(n+1))
[A101563(n) for n in range(41)] # G. C. Greubel, Jun 25 2024

Crossrefs

Cf. A051731, A081295, A048272, A101561, A101562.

Sequence in context: A360348 A174509 A103461 * A269732 A007133 A183518

Adjacent sequences: A101560 A101561 A101562 * A101564 A101565 A101566

Keyword

easy,nonn,changed

Author

Paul Barry, Dec 07 2004

Status

approved