A021279 Expansion of 1/((1-x)(1-2x)(1-8x)(1-12x)).

1, 23, 371, 5227, 68955, 877371, 10927867, 134329979, 1637524859, 19854820219, 239894019963, 2891817662331, 34806527338363, 418516051199867, 5028894399547259, 60400347075823483, 725233079160063867

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-158,328,-192).

Formula

a(n) = (21*12^(n+3) - 55*8^(n+3) + 154*2^(n+3) - 120)/9240. - Yahia Kahloune, Jul 08 2013

a(0)=1, a(1)=23, a(2)=371, a(3)=5227; for n >3, a(n) = 23*a(n-1) -158*a(n-2) +328*a(n-3) -192*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=23; for n>1, a(n) = 20*a(n-1) -96*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{23, -158, 328, -192}, {1, 23, 371, 5227}, 30] (* Harvey P. Dale, Feb 11 2015 *)

Prog

(Magma) I:=[1, 23, 371, 5227]; [n le 4 select I[n] else 23*Self(n-1)-158*Self(n-2)+328*Self(n-3)-192*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-12*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A021294 A019628 A018091 * A018071 A016325 A016324

Adjacent sequences: A021276 A021277 A021278 * A021280 A021281 A021282

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved