A026857 a(n) = T(2n+1,n+4), T given by A026736.

1, 9, 55, 287, 1381, 6343, 28313, 124083, 537242, 2307118, 9852240, 41910428, 177807902, 752981956, 3184773246, 13459063660, 56849094136, 240047748038, 1013452871316, 4278470305930, 18062827159136, 76263743441314, 322033566728056

Offset

3,2

Links

G. C. Greubel, Table of n, a(n) for n = 3..1000

Formula

G.f.: x^3*C(x)^8/(1 - x/sqrt(1-4*x)). - G. C. Greubel, Jul 19 2019

a(n) ~ phi^(3*n-4) / sqrt(5), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 19 2019

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4x])^8/(2^8*x^5*(1-x/Sqrt[1-4x])), {x, 0, 40}], x], 3] (* G. C. Greubel, Jul 19 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1-sqrt(1-4*x))^8/(2^8*x^5*(1-x/sqrt(1-4*x)))) \\ G. C. Greubel, Jul 19 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^8/(2^8*x^5*(1-x/Sqrt(1-4*x))) )); // G. C. Greubel, Jul 19 2019
(Sage) a=((1-sqrt(1-4*x))^8/(2^8*x^5*(1-x/sqrt(1-4*x)))).series(x, 45).coefficients(x, sparse=False); a[3:40] # G. C. Greubel, Jul 19 2019

Crossrefs

Cf. A000108, A026736.

Sequence in context: A005770 A030053 A072844 * A244650 A097790 A356339

Adjacent sequences: A026854 A026855 A026856 * A026858 A026859 A026860

Keyword

nonn

Author

Clark Kimberling

Status

approved