A021224 Expansion of 1/((1-x)(1-2x)(1-7x)(1-8x)).

1, 18, 221, 2322, 22485, 207306, 1850557, 16149474, 138611429, 1174801914, 9859790733, 82107957906, 679471095733, 5594020809642, 45859930816349, 374633796970818, 3051350828977797, 24790769804563290

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,-103,198,-112).

Formula

a(n)=(5*8^(n+3) - 7^(n+4) + 7*2^(n+3) - 5)/210. [Yahia Kahloune, Jun 26 2013]

a(0)=1, a(1)=18, a(2)=221, a(3)=2322; for n>3, a(n) = 18*a(n-1) -103*a(n-2) +198*a(n-3) -112*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=18; for n>1, a(n) = 15*a(n-1) -56*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)

Prog

(Magma) I:=[1, 18, 221, 2322]; [n le 4 select I[n] else 18*Self(n-1)-103*Self(n-2)+198*Self(n-3)-112*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-8*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A224296 A019333 A021454 * A017997 A018911 A021194

Adjacent sequences: A021221 A021222 A021223 * A021225 A021226 A021227

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved