A016849 Expansion of 1/((1-3x)(1-4x)(1-8x)).

1, 15, 157, 1431, 12229, 101199, 823789, 6649287, 53436757, 428483583, 3431885821, 27471332343, 219836173285, 1758953038767, 14072683703053, 112585721544999, 900702823089013, 7205690916768351, 57645801049792285

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,-68,96).

Formula

a(n) = 15*a(n-1) - 68*a(n-2) + 96*a(n-3); a(0)=1, a(1)=15, a(2)=157. - Harvey P. Dale, Mar 23 2012

a(n) = 9*3^n/5 - 4*4^n + 16*8^n/5. - R. J. Mathar, Jun 23 2013

a(n) = 12*a(n-1) - 32*a(n-2) + 3^n. - Vincenzo Librandi, Jun 26 2013

Mathematica

CoefficientList[Series[1/((1-3x)(1-4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -68, 96}, {1, 15, 157}, 30] (* Harvey P. Dale, Mar 23 2012 *)

Prog

(Magma) I:=[1, 15, 157]; [n le 3 select I[n] else 15*Self(n-1)-68*Self(n-2) +96*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)*(1-8*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-4*x)*(1-8*x))) \\ Altug Alkan, Sep 23 2018

Crossrefs

Sequence in context: A099915 A110557 A016304 * A300077 A367497 A232414

Adjacent sequences: A016846 A016847 A016848 * A016850 A016851 A016852

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved