A026743 a(n) = Sum_{j=0..n} T(n,j), T given by A026736.

1, 2, 4, 8, 17, 34, 73, 146, 314, 628, 1350, 2700, 5798, 11596, 24872, 49744, 106573, 213146, 456169, 912338, 1950697, 3901394, 8334539, 16669078, 35582783, 71165566, 151809737, 303619474, 647279131, 1294558262, 2758310121

Offset

0,2

Links

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

Formula

G.f.: ((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1 -4*x^2 - x^4)). - David Callan, Jan 17 2016

Conjecture D-finite with recurrence n*a(n) -2*a(n-1) +(-11*n+20)*a(n-2) +14*a(n-3) +(39*n-152)*a(n-4) -22*a(n-5) +(-41*n+268)*a(n-6) -6*a(n-7) +12*(-n+6)*a(n-8)=0. - R. J. Mathar, Jan 13 2023

a(n) ~ ((1 + (-1)^n)*phi^(3/2) + 2*(1 - (-1)^n)) * phi^((3*n + 1)/2) / (2*sqrt(5)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Mar 08 2023

Mathematica

CoefficientList[Normal[Series[((1-3x^2)Sqrt[(1+2x)/(1-2x)] +(1 + 2x)(1+ x^2))/(2(1-4x^2-x^4)), {x, 0, 40}]], x] (* David Callan, Jan 17 2016 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4))) \\ G. C. Greubel, Jul 16 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( ((1 -3*x^2)*Sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4)) )); // G. C. Greubel, Jul 16 2019
(Sage) (((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1-4*x^2 - x^4))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 16 2019

Crossrefs

Cf. A026736.

Sequence in context: A266446 A018093 A214083 * A026392 A266897 A018094

Adjacent sequences: A026740 A026741 A026742 * A026744 A026745 A026746

Keyword

nonn

Author

Clark Kimberling

Status

approved