OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..487
FORMULA
Recurrence: see Maple program.
a(n) ~ sqrt((6 + 5*2^(1/3) + 4*2^(2/3))/6) * (24*2^(2/3) + 30*2^(1/3) + 38)^n / (4*Pi*n). - Vaclav Kotesovec, May 14 2020
G.f.: (1+hypergeom([1/3, 2/3],[1],108*x/(1-2*x)^3)/(1-2*x))/2. - Mark van Hoeij, Nov 28 2024
MAPLE
a:= proc(n) option remember; `if`(n<4, [1, 13, 818, 64324][n+1],
(2*(3*n-2)*(57*n^2-95*n+25)*a(n-1)-4*(9*n^3-30*n^2+29*n-6)*
a(n-2)+8*(3*n-1)*(n-2)^2*a(n-3))/(n^2*(3*n-4)))
end:
seq(a(n), n=0..20);
MATHEMATICA
a[n_] := a[n] = If[n < 4, {1, 13, 818, 64324}[[n+1]], (2(3n-2)(57n^2- 95n+25) a[n-1] - 4(9n^3-30n^2+29n-6) a[n-2] + 8(3n-1)(n-2)^2 a[n-3]) / (n^2 (3n-4))];
a /@ Range[0, 20] (* Jean-François Alcover, May 14 2020, after Maple *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Jul 10 2018
STATUS
approved