A017389 Expansion of 1/((1-3x)(1-5x)(1-7x)).

1, 15, 154, 1350, 10891, 83685, 623764, 4558380, 32875381, 234980955, 1669192174, 11806149810, 83252603071, 585817587825, 4115974729384, 28888095527640, 202598073849961, 1420093671872295, 9950191865139394

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-71,105)

Formula

From Vincenzo Librandi, Jun 26 2013: (Start)

a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3).

a(n) = 12*a(n-1) - 35*a(n-2) + 3^n. (End)

a(n) = (7^(n+2) - 2*5^(n+2) + 3^(n+2))/8. - Yahia Kahloune, Aug 13 2013

Maple

A017389:=n->(7^(n+2) - 2*5^(n+2) + 3^(n+2))/8: seq(A017389(n), n=0..20); # Wesley Ivan Hurt, Mar 25 2014

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)

Prog

(Magma) I:=[1, 15, 154]; [n le 3 select I[n] else 15*Self(n-1)-71*Self(n-2)+105*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-7*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) a(n) = (7^(n+2) - 2*5^(n+2) + 3^(n+2))/8; \\ Joerg Arndt, Aug 13 2013
(PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-5*x)*(1-7*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A010035 A370765 A334356 * A278803 A157380 A098685

Adjacent sequences: A017386 A017387 A017388 * A017390 A017391 A017392

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved