A026843 a(n) = T(2n,n+3), T given by A026725.

1, 8, 46, 233, 1108, 5083, 22805, 100827, 441311, 1917751, 8289965, 35694218, 153225617, 656213596, 2805143526, 11973556060, 51047361676, 217420991444, 925300665762, 3935293406942, 16727533586006, 71069911887898, 301835332909216

Offset

3,2

Comments

Column k=7 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

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

Formula

G.f.: (x^3*C(x)^7)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - Philippe Deléham, Feb 02 2014

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[1-4*x])^7/(16*x^2*(8*x^2 -(1-Sqrt[1-4*x])^3)), {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))^7/(16*x^2*(8*x^2 -(1-sqrt(1-4*x))^3)) ) \\ G. C. Greubel, Jul 19 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^7/(16*x^2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 19 2019
(Sage) a=((1-sqrt(1-4*x))^7/(16*x^2*(8*x^2 -(1-sqrt(1-4*x))^3)) ).series(x, 45).coefficients(x, sparse=False); a[3:40] # G. C. Greubel, Jul 19 2019

Crossrefs

Cf. A000108, A026725, A236830.

Sequence in context: A172064 A197238 A182542 * A026874 A190866 A026867

Adjacent sequences: A026840 A026841 A026842 * A026844 A026845 A026846

Keyword

nonn

Author

Clark Kimberling

Status

approved