A021044 Expansion of 1/((1-x)(1-2x)(1-3x)(1-8x)).

1, 14, 137, 1186, 9789, 79278, 637249, 5107322, 40887077, 327183142, 2617726761, 20942603058, 167543199565, 1340352738206, 10722843363473, 85782811346794, 686262684222453, 5490102054386070, 43920818177432185, 351366550647536930, 2810932420866630941

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-59,94,-48).

Formula

a(n) = -(1/14)+(4/3)*2^n-(27/10)*3^n+(256/105)*8^n. - Antonio Alberto Olivares, May 12, 2012

a(0)=1, a(1)=14; for n>1, a(n) = 11*a(n-1) -24*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=14, a(2)=137, a(3)=1186; for n>3, a(n) = 14*a(n-1) -59*a(n-2) +94*a(n-3) -48*a(n-4). - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)
LinearRecurrence[{14, -59, 94, -48}, {1, 14, 137, 1186}, 30] (* Harvey P. Dale, Mar 31 2018 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-8*x)))); /* or */ I:=[1, 14, 137, 1186]; [n le 4 select I[n] else 14*Self(n-1)-59*Self(n-2)+94*Self(n-3)-48*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A306301 A155625 A016296 * A338323 A121034 A374513

Adjacent sequences: A021041 A021042 A021043 * A021045 A021046 A021047

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved