A019672 Expansion of 1/((1-4x)(1-8x)(1-11x)).

1, 23, 365, 4975, 62661, 753783, 8811805, 101107775, 1145674421, 12870591943, 143722946445, 1598128085775, 17716831119781, 195984586836503, 2164626279788285, 23881256748106975, 263256769887630741

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,-164,352).

Formula

a(n)= 11^(n+2)/21 -2*8^(n+1)/3 +4^(n+1)/7. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=23, a(2)=365; for n>2, a(n) = 23*a(n-1) -164*a(n-2) +352*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 19*a(n-1) -88*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 8 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-8*x)*(1-11*x)))); /* or */ I:=[1, 23, 365]; [n le 3 select I[n] else 23*Self(n-1)-164*Self(n-2)+352*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A202666 A019682 A021844 * A021629 A019869 A021294

Adjacent sequences: A019669 A019670 A019671 * A019673 A019674 A019675

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved