OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..600
Wikipedia, Counting lattice paths
MAPLE
b:= proc(x, y) option remember; `if`(y=0, [1$2], (p-> p+[0, p[1]])(
add(add(`if`((h=1 or isprime(h)) and (v=1 or isprime(v)),
b(sort([x-h, y-v])[]), 0), v=1..y), h=1..x)))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..30);
MATHEMATICA
f[p_List] := p + {0, p[[1]]}; f[0] = 0;
b[{x_, y_}] := b[{x, y}] = If[y == 0, {1, 1}, f[
Sum[Sum[If[(h == 1 || PrimeQ[h]) && (v == 1 || PrimeQ[v]),
b[Sort@{x - h, y - v}], {0, 0}], {v, 1, y}], {h, 1, x}]]];
a[n_] := b[{n, n}][[2]];
a /@ Range[0, 30] (* Jean-François Alcover, Apr 05 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 16 2019
STATUS
approved