A016248 Expansion of 1/((1-x)(1-6x)(1-12x)).

1, 19, 271, 3511, 43687, 533575, 6458887, 77842567, 936126343, 11245609351, 135019871623, 1620673815943, 19450697930119, 233424047994247, 2801182612927879, 33614755577116039, 403380452257281415

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (19,-90,72).

Formula

a(0)=1, a(1)=19, a(n)=18*a(n-1)-72*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(n) = (5*12^(n+2) - 11*6^(n+2) + 6)/330. [Yahia Kahloune, Aug 13 2013]

Maple

a:=n->sum((12^(n-j)-6^(n-j))/6, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 12 2007

Mathematica

CoefficientList[Series[1/((1-x)(1-6x)(1-12x)), {x, 0, 20}], x] (* Harvey P. Dale, Jan 04 2026 *)
(* Alternative: *)
LinearRecurrence[{19, -90, 72}, {1, 19, 271}, 20] (* Harvey P. Dale, Jan 04 2026 *)

Prog

(PARI) a(n) = (5*12^(n+2) - 11*6^(n+2) + 6)/330; \\ Joerg Arndt, Aug 13 2013

Crossrefs

Sequence in context: A139739 A016189 A125476 * A322539 A199819 A016187

Adjacent sequences: A016245 A016246 A016247 * A016249 A016250 A016251

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved