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A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n. 7
8, 79, 717, 6458, 58126, 523137, 4708235, 42374116, 381367044, 3432303395, 30890730553, 278016574974, 2502149174762, 22519342572853, 202674083155671, 1824066748401032, 16416600735609280, 147749406620483511, 1329744659584351589, 11967701936259164290 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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. A014832.
Sequence in context: A366214 A061425 A160605 * A224759 A024102 A034355
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 23 2022
STATUS
approved

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)