A020968 Expansion of 1/((1-7*x)*(1-8*x)*(1-11*x)).

1, 26, 455, 6700, 89661, 1130766, 13712035, 161844800, 1874156921, 21406992706, 242089527615, 2717862993300, 30349359729781, 337562780465846, 3743627395703195, 41428143398876200, 457728746687336241

Offset

0,2

Links

Indranil Ghosh, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (26,-221,616).

Formula

a(n) = 26*a(n-1) - 221*a(n-2) + 616*a(n-3) for n>=3. - Vincenzo Librandi, Mar 15 2011

a(n) = 19*a(n-1) - 88*a(n-2) + 7^n for n>1, a(0)=1, a(1)=26. - Vincenzo Librandi, Mar 15 2011

a(n) = (3*7^(n+2) - 4*8^(n+2) + 11^(n+2))/12. - Bruno Berselli, Mar 15 2011

Mathematica

Table[(3 7^(n + 2) - 4 8^(n + 2) + 11^(n + 2))/12, {n, 0, 16}] (* or *) CoefficientList[Series[1/((1 - 7 x) (1 - 8 x) (1 - 11 x)), {x, 0, 16}], x] (* Indranil Ghosh, Feb 28 2017 *)
LinearRecurrence[{26, -221, 616}, {1, 26, 455}, 20] (* Harvey P. Dale, Dec 24 2020 *)

Prog

(PARI) a(n) = (3*7^(n+2)-4*8^(n+2)+11^(n+2))/12; \\ Indranil Ghosh, Feb 28 2017
(Python) def A020968(n): return (3*7**(n+2)-4*8**(n + 2)+11**(n+2))//12 # Indranil Ghosh, Feb 28 2017
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-8*x)*(1-11*x)))); // G. C. Greubel, May 31 2018

Crossrefs

Sequence in context: A025979 A020970 A023953 * A025955 A022725 A020606

Adjacent sequences: A020965 A020966 A020967 * A020969 A020970 A020971

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved