A047085 a(n) = T(2*n, n), array T as in A047080.

1, 1, 3, 9, 27, 83, 259, 817, 2599, 8323, 26797, 86659, 281287, 915907, 2990383, 9786369, 32092959, 105435607, 346950321, 1143342603, 3772698725, 12463525229, 41218894577, 136451431723, 452116980643, 1499282161375, 4975631425581, 16524213199923, 54913514061867

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A047080, A047081, A047082, A047083, A047084, A047086, A047087, A047088.

Cf. A171155.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 50); Coefficients(R!( Sqrt((1-x)/(1 -3*x-x^2-x^3)) )); // G. C. Greubel, Oct 30 2022

Mathematica

CoefficientList[Series[Sqrt[(1-x)/(1-3*x-x^2-x^3)], {x, 0, 50}], x] (* G. C. Greubel, Oct 30 2022 *)

SageMath

def A047085_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( sqrt((1-x)/(1-3*x-x^2-x^3)) ).list()
A047085_list(50) # G. C. Greubel, Oct 30 2022

Formula

From G. C. Greubel, Oct 30 2022: (Start)

a(n) = A171155(n).

G.f.: sqrt((1 - x)/(1 - 3*x - x^2 - x^3)). (End)

Extensions

Data corrected by Sean A. Irvine, May 11 2021