A017269 Expansion of 1/((1-3x)(1-5x)(1-6x)).

1, 14, 133, 1070, 7861, 54614, 365653, 2385950, 15282421, 96547814, 603612373, 3743478830, 23070427381, 141471930614, 864083198293, 5260771611710, 31946034826741, 193583363883014, 1171036345331413

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-63,90).

Formula

From Vincenzo Librandi, Jun 26 2013: (Start)

a(n) = 14*a(n-1) - 63*a(n-2) + 90*a(n-3).

a(n) = 11*a(n-1) - 30*a(n-2) + 3^n. (End)

a(n) = (2*6^(n+2) - 3*5^(n+2) + 3^(n+2))/6. - Yahia Kahloune, Aug 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)
LinearRecurrence[{14, -63, 90}, {1, 14, 133}, 30] (* Harvey P. Dale, Sep 20 2013 *)

Prog

(Magma) I:=[1, 14, 133]; [n le 3 select I[n] else 14*Self(n-1)-63*Self(n-2)+90*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-6*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-5*x)*(1-6*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A328785 A113976 A022738 * A021079 A174563 A233467

Adjacent sequences: A017266 A017267 A017268 * A017270 A017271 A017272

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved