A021164 Expansion of 1/((1-x)*(1-2*x)*(1-5*x)*(1-12*x)).

1, 20, 287, 3694, 45609, 553776, 6677779, 80295938, 964364717, 11576444932, 138937682871, 1667353916982, 20008755624625, 240107610616088, 2881304043028763, 34575712094589226, 414908863026422133

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,-113,214,-120).

Formula

a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -60*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=20, a(2)=287, a(3)=3694; for n>3, a(n) = 20*a(n-1) -113*a(n-2) +214*a(n-3)-120*a(n-4). - Vincenzo Librandi, Jul 07 2013

a(n) = (6*12^(n+3) - 11*5^(n+4) + 77*2^(n+4) - 105)/4620. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 -  12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{20, -113, 214, -120}, {1, 20, 287, 3694}, 20] (* Harvey P. Dale, Nov 15 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-12*x)))); /* or */ I:=[1, 20, 287, 3694]; [n le 4 select I[n] else 20*Self(n-1)-113*Self(n-2)+214*Self(n-3)-120*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A046175 A231105 A016314 * A225829 A017918 A329710

Adjacent sequences: A021161 A021162 A021163 * A021165 A021166 A021167

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved