A021244 Expansion of 1/((1-x)(1-2x)(1-7x)(1-11x)).

1, 21, 308, 3942, 47271, 547407, 6213586, 69694464, 776054741, 8602512633, 95089014384, 1049208790266, 11563904125411, 127361197423299, 1402080935995502, 15430644646390548, 169791371563507281

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-133,267,-154).

Formula

a(n)=(11^(n+3) - 3*7^(n+3) + 8*2^(n+3) - 6)/360. [Yahia Kahloune, Jun 30 2013]

a(0)=1, a(1)=21, a(2)=308, a(3)=3942; for n>3, a(n) = 21*a(n-1) -133*a(n-2) +267*a(n-3) -154*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -77*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{21, -133, 267, -154}, {1, 21, 308, 3942}, 20] (* Harvey P. Dale, May 31 2020 *)

Prog

(Magma) I:=[1, 21, 308, 3942]; [n le 4 select I[n] else 21*Self(n-1)-133*Self(n-2)+267*Self(n-3)-154*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-11*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A018069 A019488 A025929 * A183463 A125478 A018054

Adjacent sequences: A021241 A021242 A021243 * A021245 A021246 A021247

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved