A021094 Expansion of 1/((1-x)(1-2x)(1-4x)(1-11x)).

1, 18, 233, 2718, 30549, 338706, 3736561, 41145606, 452775917, 4981233114, 54796358409, 602771123214, 6630527086405, 72935976891042, 802296461596577, 8825263940808342, 97077914802006813, 1067857108634797290

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-91,162,-88).

Formula

a(n) = -(1/30)+(4/9)*2^n-(32/21)*4^n+(1331/630)*11^n. [Antonio Alberto Olivares, May 22 2012]

a(0)=1, a(1)=18; for n>1, a(n) = 15*a(n-1) -44*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 06 2013

a(0)=1, a(1)=18, a(2)=233, a(3)=2718; for n>3, a(n) = 18*a(n-1) -91*a(n-2) +162*a(n-3) -88*a(n-4). - Vincenzo Librandi, Jul 06 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 06 2013 *)
LinearRecurrence[{18, -91, 162, -88}, {1, 18, 233, 2718}, 20] (* Robert G. Wilson v, Jul 06 2013 *)

Prog

(Magma) I:=[1, 18, 233, 2718]; [n le 4 select I[n] else 18*Self(n-1)-91*Self(n-2)+162*Self(n-3)-88*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-11*x)))); // Vincenzo Librandi, Jul 06 2013

Crossrefs

Sequence in context: A017916 A016307 A193982 * A275963 A125453 A016256

Adjacent sequences: A021091 A021092 A021093 * A021095 A021096 A021097

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved