OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..700
FORMULA
For n>0, a(n) = binomial(3*n+1, n+1)*binomial(2*n, n) + binomial(3*n+1, n-1). - Vaclav Kotesovec, Sep 20 2019
EXAMPLE
a(0) = 1: [1].
a(1) = 13: [1/4,1/4,1/4,1/4], [1/2,1/4,1/8,1/8], [1/2,1/8,1/4,1/8], [1/2,1/8,1/8,1/4], [1/4,1/2,1/8,1/8], [1/4,1/8,1/2,1/8], [1/4,1/8,1/8,1/2], [1/8,1/2,1/4,1/8], [1/8,1/2,1/8,1/4], [1/8,1/4,1/2,1/8], [1/8,1/4,1/8,1/2], [1/8,1/8,1/2,1/4], [1/8,1/8,1/4,1/2].
MAPLE
a:= proc(n) option remember; `if`(n<2, 12*n+1, (3*n-1)*(3*n+1)*
3*((15*n^3-31*n^2-4*n+8)*n*a(n-1)-3*(3*n-4)*(3*n-2)*
(3*n^2-2*n-2)*a(n-2))/((n+1)*(4*n+2)*(3*n^2-8*n+3)*n^2))
end:
seq(a(n), n=0..20);
MATHEMATICA
a[n_] := a[n] = If[n < 2, 12*n + 1, (3*n - 1)*(3*n + 1)*3*((15*n^3 - 31*n^2 - 4*n + 8)*n*a[n-1] - 3*(3*n - 4)*(3*n - 2)*(3*n^2 - 2*n - 2)*a[n-2])/((n + 1)*(4*n + 2)*(3*n^2 - 8*n + 3)*n^2)];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
Table[Binomial[3*n + 1, n + 1]*Binomial[2*n, n] + Binomial[3*n + 1, n - 1], {n, 0, 20}] (* Vaclav Kotesovec, Sep 20 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 12 2017
STATUS
approved