A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.

8, 79, 717, 6458, 58126, 523137, 4708235, 42374116, 381367044, 3432303395, 30890730553, 278016574974, 2502149174762, 22519342572853, 202674083155671, 1824066748401032, 16416600735609280, 147749406620483511, 1329744659584351589, 11967701936259164290

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Formula

G.f.: x * (8 - 9 * x)/((1 - x)^2 * (1 - 9 * x)).

a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).

a(n) = 7 * A014832(n) + n.

a(n) = (7*9^(n+1) + 8*n - 63)/64.

a(n) = Sum_{k=0..n-1} (9 - n + k)*9^k.

E.g.f.: exp(x)*(63*(exp(8*x) - 1) + 8*x)/64. - Stefano Spezia, May 29 2023

Mathematica

LinearRecurrence[{11, -19, 9}, {8, 79, 717}, 20] (* Amiram Eldar, Apr 23 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(x*(8-9*x)/((1-x)^2*(1-9*x)))
(PARI) a(n) = (7*9^(n+1)+8*n-63)/64;
(PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 9);

Crossrefs

Cf. A064617, A353094, A353095, A353096, A353097, A353098, A353099.

Cf. A014832.

Sequence in context: A366214 A061425 A160605 * A224759 A024102 A034355

Adjacent sequences: A353097 A353098 A353099 * A353101 A353102 A353103

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 23 2022

Status

approved