A020499 Expansion of 1/((1-5x)(1-9x)(1-11x)).

1, 25, 426, 6170, 81851, 1029315, 12498676, 148149460, 1726010901, 19855374605, 226242178526, 2559210312750, 28786474721551, 322368894171895, 3597522989519976, 40035969784960040, 444564772324613801

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-199,495).

Formula

a(n) = 25*5^n/24 -81*9^n/8 +121*11^n/12. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=25, a(2)=426; for n>2, a(n) = 25*a(n-1) -199*a(n-2) +495*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 20*a(n-1) -99*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{25, -199, 495}, {1, 25, 426}, 20] (* Harvey P. Dale, Feb 27 2023 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 25, 426]; [n le 3 select I[n] else 25*Self(n-1)-199*Self(n-2)+495*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A025951 A021944 A299845 * A226712 A020577 A021714

Adjacent sequences: A020496 A020497 A020498 * A020500 A020501 A020502

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved