A021264 Expansion of 1/((1-x)(1-2x)(1-8x)(1-9x)).

1, 20, 275, 3250, 35481, 369240, 3722575, 36698750, 355853861, 3407206660, 32301037275, 303798758250, 2838904214641, 26387861071280, 244192534790375, 2251347094369750, 20691038099509821, 189650656897307100

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-125,250,-144).

Formula

a(0)=1, a(1)=20, a(2)=275; a(n)=(3*9^(n+3) - 4*8^(n+3) + 2^(n+5) - 3)/168. [Yahia Kahloune, Jun 21 2013]

a(0)=1, a(1)=20, a(2)=275, a(3)=3250; for n>3, a(n) = 20*a(n-1) -125*a(n-2) +250*a(n-3) -144*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -72*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{20, -125, 250, -144}, {1, 20, 275, 3250}, 20] (* Harvey P. Dale, Mar 04 2019 *)

Prog

(Magma) I:=[1, 20, 275, 3250]; [n le 4 select I[n] else 20*Self(n-1)-125*Self(n-2)+250*Self(n-3)-144*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-9*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A021514 A121117 A278722 * A025928 A004334 A019483

Adjacent sequences: A021261 A021262 A021263 * A021265 A021266 A021267

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved