A234276 G.f.: 1/(1-(2*x^2+x^3)*(1-sqrt(1-4*x))).

1, 0, 0, 4, 6, 10, 40, 114, 312, 988, 3184, 10330, 34516, 117620, 406204, 1421132, 5027504, 17950224, 64605044, 234157026, 853907268, 3130879580, 11534945108, 42681346612, 158542854496, 590990616384, 2210044475416, 8288715167044, 31169768849048, 117502527712360, 443962154618072, 1680957824494200

Offset

0,4

Links

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

R. De Castro, A. L. Ramírez and J. L. Ramírez, Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs, arXiv:1310.2449 [cs.DM], 2013

Formula

a(n) ~ 9*2^(2*n+5)/(3025*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Dec 26 2013

D-finite with recurrence: 2*(-n+2)*a(n) +(7*n-24)*a(n-1) +2*(6*n-19)*a(n-2) +8*(-3*n+11)*a(n-3) +2*(-15*n+68)*a(n-4) +4*(-10*n+27)*a(n-5) +80*(n-4)*a(n-6) +24*(7*n-30)*a(n-7) +4*(23*n-112)*a(n-8) +8*(2*n-11)*a(n-9)=0. - R. J. Mathar, Jan 25 2020

Mathematica

CoefficientList[Series[1/(1 - (2*x^2 + x^3)*(1 - Sqrt[1 - 4*x])), {x, 0, 50}], x] (* G. C. Greubel, Jun 01 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1-(2*x^2+x^3)*(1-sqrt(1-4*x)))) \\ G. C. Greubel, Jun 01 2017

Crossrefs

Sequence in context: A271956 A242502 A136838 * A274991 A356755 A109378

Adjacent sequences: A234273 A234274 A234275 * A234277 A234278 A234279

Keyword

nonn

Author

N. J. A. Sloane, Dec 25 2013

Status

approved