A120664 Expansion of 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3).

0, 2, 4, 18, 92, 442, 2004, 8738, 37132, 155082, 640004, 2619058, 10653372, 43144922, 174174004, 701478978, 2820264812, 11324105962, 45425564004, 182089676498, 729520967452, 2921570654202, 11696742970004, 46818352939618

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

From Colin Barker, Aug 02 2012: (Start)

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n > 3.

G.f.: 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3). (End)

Mathematica

LinearRecurrence[{8, -19, 12}, {0, 2, 4, 18}, 31] (* G. C. Greubel, Dec 26 2022 *)

Prog

(Magma) I:=[2, 4, 18]; [0] cat [n le 3 select I[n] else 8*Self(n-1) -19*Self(n-2) +12*Self(n-3): n in [1..31]]; // G. C. Greubel, Dec 26 2022
(SageMath)
@CachedFunction
def a(n): # a = A120664
    if (n<4): return (0, 2, 4, 18)[n]
    else: return 8*a(n-1) -19*a(n-2) +12*a(n-3)
[a(n) for n in range(41)] # G. C. Greubel, Dec 26 2022

Crossrefs

Sequence in context: A075836 A295370 A292280 * A095816 A020101 A370524

Adjacent sequences: A120661 A120662 A120663 * A120665 A120666 A120667

Keyword

nonn,easy,less

Author

Roger L. Bagula, Aug 11 2006

Extensions

Edited by N. J. A. Sloane, Jul 13 2007

New name from Colin Barker, Aug 02 2012

Status

approved