A084683 Expansion of g.f.: (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)).

1, 2, 4, 8, 14, 24, 40, 65, 104, 164, 258, 404, 632, 986, 1537, 2394, 3728, 5804, 9034, 14060, 21880, 34049, 52984, 82448, 128294, 199632, 310636, 483362, 752129, 1170338, 1821084, 2833664, 4409270, 6860960, 10675864, 16611969, 25848728, 40221404, 62585722, 97385276

Offset

0,2

Links

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

J. Hietarinta and C.-M. Viallet, Discrete Painlevé I and singularity confinement in projective space, Chaos, Solitons and Fractals 11, 2000, p. 29.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,0,-2,1).

Mathematica

CoefficientList[Series[(1+2x^3+2x^6)/((1-x)(1-x-x^2+x^3-x^4-x^5+x^6)), {x, 0, 60}], x] (* or *) LinearRecurrence[{2, 0, -2, 2, 0, -2, 1}, {1, 2, 4, 8, 14, 24, 40}, 60] (* Harvey P. Dale, Jun 23 2018 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)) )); // G. C. Greubel, Mar 22 2023
(SageMath)
def A084683_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+2*x^3+2*x^6)/((1-x)*(1-x-x^2+x^3-x^4-x^5+x^6)) ).list()
A084683_list(60) # G. C. Greubel, Mar 22 2023

Crossrefs

Cf. A064864.

Sequence in context: A015128 A208605 A123655 * A271493 A118544 A222037

Adjacent sequences: A084680 A084681 A084682 * A084684 A084685 A084686

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 16 2003

Status

approved