A022111 Expansion of 1/((1-x)(1-5x)(1-6x)(1-8x)).

1, 20, 263, 2878, 28449, 264048, 2350651, 20332466, 172311557, 1438844836, 11885079999, 97387603014, 793247778025, 6432389826584, 51985193621507, 419076145997722, 3371967484999053, 27092843456412492

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (20,-137,358,-240)

Formula

a(n) = 256*8^n/21 -108*6^n/5 + 125*5^n/12 -1/140. - R. J. Mathar, Mar 11 2011

a(0)=1, a(1)=20, a(2)=263, a(3)=2878, a(n)=20*a(n-1)-137*a(n-2)+ 358*a(n-3)- 240*a(n-4). - Harvey P. Dale, Nov 04 2012

Mathematica

CoefficientList[Series[1/((1-x)(1-5x)(1-6x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -137, 358, -240}, {1, 20, 263, 2878}, 30] (* Harvey P. Dale, Nov 04 2012 *)

Prog

(Magma) I:=[1, 20, 263, 2878]; [n le 4 select I[n] else 20*Self(n-1)-137*Self(n-2)+358*Self(n-3)-240*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-8*x)))); // Vincenzo Librandi, Jul 12 2013

Crossrefs

Sequence in context: A025966 A356837 A041764 * A025943 A025961 A208948

Adjacent sequences: A022108 A022109 A022110 * A022112 A022113 A022114

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved