A373245 - OEIS

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A373245

Binomial transform of A135318.

1, 2, 4, 9, 22, 55, 136, 331, 798, 1919, 4620, 11143, 26906, 64987, 156944, 378939, 914822, 2208455, 5331476, 12871151, 31073778, 75019219, 181113240, 437246723, 1055606686, 2548458047, 6152518684, 14853491319, 35859501322, 86572502155, 209004522016

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2,2).

FORMULA

G.f.: (1 - 2*x + x^2 + x^3)/((1 - 2*x - x^2)*(1 - 2*x + 2*x^2)). - Vaclav Kotesovec, May 29 2024

a(n) = A114203(n+1)/2. - Hugo Pfoertner, May 29 2024

E.g.f.: exp(x)*(2*cos(x) + 4*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))/6. - Stefano Spezia, May 29 2024

MATHEMATICA

CoefficientList[Series[(1 - 2*x + x^2 + x^3)/((1 - 2*x - x^2)*(1 - 2*x + 2*x^2)), {x, 0, 30}], x] (* Vaclav Kotesovec, May 29 2024 *)