A019041 Expansion of 1/((1-4x)(1-5x)(1-12x)).

1, 21, 313, 4125, 51601, 630741, 7630633, 91892685, 1104403201, 13261555461, 159183299353, 1910426955645, 22926277062001, 275121159824181, 3301483361726473, 39617948633641005, 475416129363276001

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-128,240).

Formula

a(n) = 2*4^n - 25*5^n/7 + 18*12^n/7. - R. J. Mathar, Jun 29 2013

From Vincenzo Librandi, Jul 02 2013: (Start)

a(n) = 21*a(n-1) - 128*a(n-2) + 240*a(n-3) for n > 2; a(0)=1, a(1)=21, a(2)=313.

a(n) = 17*a(n-1) - 60*a(n-2) + 4^n. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{21, -128, 240}, {1, 21, 313}, 20] (* Harvey P. Dale, Mar 09 2022 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-12*x)))); /* or */ I:=[1, 21, 313]; [n le 3 select I[n] else 21*Self(n-1)-128*Self(n-2)+240*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A157088 A226990 A016321 * A021214 A016318 A017954

Adjacent sequences: A019038 A019039 A019040 * A019042 A019043 A019044

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved