A019040 Expansion of 1/((1-4*x)*(1-5*x)*(1-11*x)).

1, 20, 281, 3460, 40161, 453300, 5048041, 55853540, 616079921, 6785596180, 74686191801, 821775473220, 9040683799681, 99453356876660, 1094016369479561, 12034328357198500, 132378357688767441, 1456165680554230740, 16017841284704959321, 176196348399674565380, 1938160304835531911201

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,-119,220).

Formula

a(n) = 16*4^n/7 - 25*5^n/6 + 121*11^n/42. - R. J. Mathar, Jun 29 2013

From Vincenzo Librandi, Jul 02 2013: (Start)

a(n) = 20*a(n-1) - 119*a(n-2) + 220*a(n-3) for n > 2; a(0)=1, a(1)=20, a(2)=281.

a(n) = 16*a(n-1) - 55*a(n-2) + 4^n. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{20, -119, 220}, {1, 20, 281}, 30] (* Harvey P. Dale, Dec 29 2024 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-11*x)))); // Vincenzo Librandi, Jul 02 2013
(Magma) I:=[1, 20, 281]; [n le 3 select I[n] else 20*Self(n-1)-119*Self(n-2)+220*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A012836 A028294 A278360 * A021204 A017953 A016317

Adjacent sequences: A019037 A019038 A019039 * A019041 A019042 A019043

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved