A021379 Expansion of 1/((1-x)*(1-3*x)*(1-4*x)*(1-9*x)).

1, 17, 198, 2002, 19019, 175539, 1598416, 14463284, 130489557, 1175715541, 10586766554, 95302471446, 857809330015, 7720634709623, 69487122519012, 625389764724088, 5628530595298793, 50656866402527385, 455912162383230190, 4103210922234398810, 36928904148481074291

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-91,183,-108).

Formula

a(0)=1, a(1)=17; for n>1, a(n) = 13*a(n-1) -36*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

a(0)=1, a(1)=17, a(2)=198, a(3)=2002; for n>3, a(n) = 17*a(n-1) -91*a(n-2) +183*a(n-3) -108*a(n-4). - Vincenzo Librandi, Jul 09 2013

a(n) = (729*9^n - 1024*4^n + 540*3^n - 5)/240. - Christian Krause, May 07 2026

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 09 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-9*x)))); // Vincenzo Librandi, Jul 09 2013
(Magma) I:=[1, 17, 198, 2002]; [n le 4 select I[n] else 17*Self(n-1)-91*Self(n-2)+183*Self(n-3)-108*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A130817 A055432 A154276 * A177075 A177076 A196491

Adjacent sequences: A021376 A021377 A021378 * A021380 A021381 A021382

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved