A019687 Expansion of 1/((1-4x)(1-9x)(1-11x)).

1, 24, 397, 5628, 73513, 914112, 11008549, 129690276, 1504024705, 17241418920, 195930981181, 2211723344844, 24837316537177, 277785786712848, 3096821665511893, 34435641499407732, 382127489397444529, 4233421296687394296, 46837804552120354285

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-179,396).

Formula

a(n) = 4^(n+2)/35 +11^(n+2)/14 -9^(n+2)/10. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=24, a(2)=397; for n>2, a(n) = 24*a(n-1) -179*a(n-2) +396*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 20*a(n-1) -99*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [24, -179, 396][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{24, -179, 396}, {1, 24, 397}, 20] (* Harvey P. Dale, Nov 16 2021 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 24, 397]; [n le 3 select I[n] else 24*Self(n-1)-179*Self(n-2)+396*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A020447 A021894 A021694 * A020341 A021674 A019677

Adjacent sequences: A019684 A019685 A019686 * A019688 A019689 A019690

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved