A026844 a(n) = T(2n,n+4), T given by A026725.

1, 10, 67, 379, 1958, 9576, 45190, 208084, 941480, 4204949, 18597694, 81635060, 356220369, 1547066801, 6693361973, 28868868733, 124194904215, 533156609953, 2284722747583, 9776008778375, 41777089615201, 178338353574365, 760586650190997

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Comments

Column k=9 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000

Crossrefs

Cf. A000108, A026725, A236830.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^9/(64*x^3*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 19 2019

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4x])^9/(64*x^3*(8*x^2-(1-Sqrt[1-4x])^3)), {x,0,40}], x], 4] (* G. C. Greubel, Jul 19 2019 *)

PARI

my(x='x+O('x^40)); Vec( (1-sqrt(1-4*x))^9/(64*x^3*(8*x^2 -(1-sqrt(1-4*x))^3)) ) \\ G. C. Greubel, Jul 19 2019

Sage

a=((1-sqrt(1-4*x))^9/(64*x^3*(8*x^2 -(1-sqrt(1-4*x))^3)) ).series(x, 45).coefficients(x, sparse=False); a[4:40] # G. C. Greubel, Jul 19 2019

Formula

G.f.: (x^4*C(x)^9)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - Philippe Deléham, Feb 02 2014

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

(7719*n+49402)*(n+3)*a(n) +(7719*n^2-1057949*n-1942990)*a(n-1) +4*(-211672*n^2+2076533*n+763807)*a(n-2) +(4326581*n^2-34087269*n+38502298)*a(n-3) +3*(-1940897*n^2+16395555*n-37085206)*a(n-4) -2*(406705*n-1575734)*(2*n-9)*a(n-5)=0. - R. J. Mathar, Oct 26 2019