A021104 Expansion of 1/((1-x)(1-2x)(1-4x)(1-12x)).

1, 19, 263, 3311, 40383, 487263, 5857951, 70338847, 844240415, 10131583007, 121581790239, 1458992663583, 17507956694047, 210095659269151, 2521148627024927, 30253786387545119, 363045448103656479

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-98,176,-96).

Formula

a(n) = -(1/33) + (2/5)*2^n - (4/3)*4^n + (108/55)*12^n. - Antonio Alberto Olivares, May 22 2012

a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -48*a(n-2)+2^n-1. - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=19, a(2)=263, a(3)=3311; for n>3, a(n) = 19*a(n-1) -98*a(n-2) +176*a(n-3) -96*a(n-4). - Vincenzo Librandi, Jul 07 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{19, -98, 176, -96}, {1, 19, 263, 3311}, 30] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-12*x)))); /* or */ I:=[1, 19, 263, 3311]; [n le 4 select I[n] else 19*Self(n-1)-98*Self(n-2)+176*Self(n-3)-96*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A142817 A294828 A016257 * A209075 A017161 A036736

Adjacent sequences: A021101 A021102 A021103 * A021105 A021106 A021107

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved