A019722 Expansion of 1/((1-4x)(1-9x)(1-12x)).

1, 25, 433, 6457, 89089, 1174537, 15047761, 189169369, 2347464097, 28866716329, 352675969009, 4288594179961, 51971489903425, 628233183645001, 7579976215410577, 91330317763703833, 1099299246068405473

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,-192,432)

Formula

a(n) = 2*4^n/5 -3^(2n+3)/5 +12^n*6. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=25, a(2)=433; for n>2, a(n) = 25*a(n-1) -192*a(n-2) +432*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 21*a(n-1) -108*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{25, -192, 432}, {1, 25, 433}, 30] (* Harvey P. Dale, Oct 30 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-12*x)))); /* or */ I:=[1, 25, 433]; [n le 3 select I[n] else 25*Self(n-1)-192*Self(n-2)+432*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A203544 A021704 A019742 * A180800 A004346 A021324

Adjacent sequences: A019719 A019720 A019721 * A019723 A019724 A019725

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved