A122109 a(n) = 9*a(n-2) - 4*a(n-3) for n > 2 with a(0)=1, a(1)=2.

1, 2, 6, 14, 46, 102, 358, 734, 2814, 5174, 22390, 35310, 180814, 228230, 1486086, 1330814, 12461854, 6032982, 106833430, 4449422, 937368942, -387288922, 8418522790, -7235076066, 77315860798, -98789775754, 724783051446, -1198371424978, 6918206566030, -13684475030586

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 (0,9,-4).

Formula

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

Maple

seq(coeff(series((1+2*x-3*x^2)/(1-9*x^2+4*x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 02 2019

Mathematica

LinearRecurrence[{0, 9, -4}, {1, 2, 6}, 30] (* G. C. Greubel, Oct 02 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+2*x-3*x^2)/(1-9*x^2+4*x^3)) \\ G. C. Greubel, Oct 02 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+2*x-3*x^2)/(1-9*x^2+4*x^3) )); // G. C. Greubel, Oct 02 2019
(Sage)
def A122109_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+2*x-3*x^2)/(1-9*x^2+4*x^3)).list()
A122109_list(30) # G. C. Greubel, Oct 02 2019
(GAP) a:=[1, 2, 6];; for n in [4..30] do a[n]:=9*a[n-2]-4*a[n-3]; od; a; # G. C. Greubel, Oct 02 2019

Crossrefs

Sequence in context: A299042 A152806 A366223 * A133155 A297708 A284701

Adjacent sequences: A122106 A122107 A122108 * A122110 A122111 A122112

Keyword

sign

Author

Philippe Deléham, Oct 18 2006

Extensions

Terms a(26) onward added by G. C. Greubel, Oct 02 2019

Status

approved