A123222 Expansion of -x * (x-1) * (3*x^2-1) / (9*x^4-8*x^3+4*x-1).

1, 3, 9, 31, 109, 391, 1397, 4995, 17833, 63675, 227313, 811543, 2897269, 10343647, 36928061, 131837979, 470678161, 1680380979, 5999172633, 21417807055, 76464283837, 272987183095, 974598829637, 3479441311347, 12422046335161

Offset: 1

Author

Roger L. Bagula, Oct 05 2006

Keywords

• nonn
• less

Links

• Index entries for linear recurrences with constant coefficients, signature (4,0,-8,9).

Crossrefs

Cf. A000952, A074872, A085340, A003432.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1))); // G. C. Greubel, Oct 12 2018

Maple

seq(coeff(series(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1),x,n+1), x, n), n = 1 .. 25); # Muniru A Asiru, Oct 13 2018

Mathematica

LinearRecurrence[{4,0,-8,9},{1,3,9,31},30] (* Harvey P. Dale, Jul 26 2018 *)

PARI

x='x+O('x^30); Vec(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1)) \\ G. C. Greubel, Oct 12 2018

Formula

From Colin Barker, Oct 19 2012: (Start)

a(n) = 4*a(n-1) -8*a(n-3) +9*a(n-4).

G.f.: -x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1). (End)

Extensions

Sequence edited by Joerg Arndt and Colin Barker, Oct 19 2012