A024114 Expansion of 1/((1-x)(1-6x)(1-8x)(1-12x)).

1, 27, 487, 7407, 102943, 1357119, 17315839, 216369279, 2667080575, 32582253951, 395677903231, 4786097041791, 57739474264447, 695339842109823, 8363901349806463, 100525966375567743, 1207588183261823359

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (27,-242,792,-576).

Formula

a(n) = (35*12^(n+3) - 165*8^(n+3) + 154*6^(n+3) - 24)/9240. [Yahia Kahloune, Jun 27 2013]

a(0)=1, a(1)=27, a(2)=487, a(3)=7407; for n>3, a(n) = 27*a(n-1) -242*a(n-2) +792*a(n-3) -576*a(n-4). - Vincenzo Librandi, Jul 16 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 16 2013 *)
LinearRecurrence[{27, -242, 792, -576}, {1, 27, 487, 7407}, 20] (* Harvey P. Dale, Jan 25 2019 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1, 27, 487, 7407]; [n le 4 select I[n] else 27*Self(n-1)-242*Self(n-2)+792*Self(n-3)-576*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Sequence in context: A025983 A081139 A020976 * A025982 A042408 A023946

Adjacent sequences: A024111 A024112 A024113 * A024115 A024116 A024117

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved