A017161 Expansion of g.f. 1/((1 - 3*x)*(1 - 4*x)*(1 - 12*x)).

1, 19, 265, 3355, 41041, 495859, 5964505, 71633035, 859838881, 10319056099, 123832690345, 1486008529915, 17832167873521, 213986278134739, 2567836397009785, 30814041016037995, 369768509243184961, 4437222179250275779, 53246666424718954825, 638959998192652301275

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-96,144).

Formula

a(n) = 3^n - 2*4^n + 2*12^n. - R. J. Mathar, Jun 23 2013

From Vincenzo Librandi, Jun 26 2013: (Start)

a(n) = 19*a(n-1) - 96*a(n-2) + 144*a(n-3).

a(n) = 16*a(n-1) - 48*a(n-2) + 3^n. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)

Prog

(Magma) I:=[1, 19, 265]; [n le 3 select I[n] else 19*Self(n-1)-96*Self(n-2)+144*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 26 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-12*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) my(x='x+O('x^20)); Vec(1/((1-3*x)*(1-4*x)*(1-12*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A016257 A021104 A209075 * A036736 A016254 A016302

Adjacent sequences: A017158 A017159 A017160 * A017162 A017163 A017164

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved