A019628 Expansion of 1/((1-4*x)*(1-7*x)*(1-12*x)).

1, 23, 369, 5143, 66977, 841575, 10367953, 126315191, 1529146113, 18443562247, 221980457777, 2668373663319, 32052757927009, 384859080003239, 4619891122628241, 55449769683406327, 665474773978915265

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,-160,336).

Formula

a(n) = 2*4^n/3 - 7^(n+2)/15 + 18*12^n/5. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=23, a(2)=369; for n>2, a(n) = 23*a(n-1) -160*a(n-2) +336*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 19*a(n-1) - 84*a(n-2) + 4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{23, -160, 336}, {1, 23, 369}, 30] (* G. C. Greubel, Jan 28 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-12*x)))); /* or */ I:=[1, 23, 369]; [n le 3 select I[n] else 23*Self(n-1)-160*Self(n-2)+336*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(PARI) x='x+O('x^30); Vec(1/((1-4*x)*(1-7*x)*(1-12*x))) \\ G. C. Greubel, Jan 28 2018

Crossrefs

Cf. A021894 (partial sums).

Sequence in context: A021629 A019869 A021294 * A018091 A021279 A018071

Adjacent sequences: A019625 A019626 A019627 * A019629 A019630 A019631

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved