A108630 Expansion of g.f.: (1+x-sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)).

1, 1, 2, 6, 17, 54, 178, 606, 2116, 7533, 27242, 99799, 369583, 1381309, 5203599, 19737935, 75321337, 288968031, 1113893815, 4312073256, 16756934181, 65345024968, 255625711296, 1002888257745, 3945055462020, 15556613282788

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Conjecture D-finite with recurrence: (n-1)*a(n) = (n-4)*a(n-1) +8*(n-4)*a(n-2) +(17*n-77)*a(n-3) +(19*n-100)*a(n-4) +12*(n-6)*a(n-5) +4*(n-7)*a(n-6). - R. J. Mathar, Sep 27 2014

Mathematica

Rest@CoefficientList[Series[(1+x-Sqrt[1-2*x-7*x^2-8*x^3-4*x^4])/(2*(1+ x+x^2)), {x, 0, 35}], x] (* G. C. Greubel, Oct 18 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 36); Coefficients(R!( (1+x-Sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)) )); // G. C. Greubel, Oct 18 2023
(Sage)
def A108630_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x-sqrt(1-2*x-7*x^2-8*x^3-4*x^4))/(2*(1+x+x^2)) ).list()
a=A108630_list(36); a[1:] # G. C. Greubel, Oct 18 2023

Crossrefs

Cf. A039985.

Sequence in context: A346428 A148453 A097514 * A338735 A161408 A150033

Adjacent sequences: A108627 A108628 A108629 * A108631 A108632 A108633

Keyword

nonn

Author

Christian G. Bower, Jun 12 2005

Status

approved