OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
MAPLE
g:= n-> (t-> `if`(issqr(t+4) or issqr(t-4), 1, 0))(5*n^2):
b:= proc(u, o, t) option remember; `if`(u+o=0, g(t),
`if`(g(t)=1, add(b(u-j, o+j-1, 1), j=1..u), 0)+
add(b(u+j-1, o-j, t+1), j=1..o))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..27);
MATHEMATICA
g[n_] := With[{t = 5n^2}, If[IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4], 1, 0]];
b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, g[t],
If[g[t] == 1, Sum[b[u - j, o + j - 1, 1], {j, 1, u}], 0] +
Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 27] (* Jean-François Alcover, Mar 29 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 21 2018
STATUS
approved