A016909 Expansion of 1/((1-3x)(1-4x)(1-9x)).

1, 16, 181, 1804, 17017, 156520, 1422877, 12864868, 116026273, 1045225984, 9411051013, 84715704892, 762506858569, 6862825379608, 61766487809389, 555902642205076, 5003140830574705, 45028335807228592

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-75,108).

Formula

a(n) = 3*3^n/2 - 16*4^n/5 + 27*9^n/10. - R. J. Mathar, Jun 23 2013

From Vincenzo Librandi, Jun 26 2013: (Start)

a(n) = 16*a(n-1) - 75*a(n-2) + 108*a(n-3).

a(n) = 13*a(n-1) - 36*a(n-2) + 3^n; a(0)=1, a(1)=16. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 4 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)

Prog

(Magma) I:=[1, 16, 181]; [n le 3 select I[n] else 16*Self(n-1)-75*Self(n-2)+108*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-9*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-4*x)*(1-9*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A269103 A016305 A218895 * A001455 A199018 A204608

Adjacent sequences: A016906 A016907 A016908 * A016910 A016911 A016912

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved