A308240 Number of lattice paths from (0,0) to (n,n) that consist of steps (h,v) with h, v prime or one.

1, 1, 2, 6, 19, 58, 184, 604, 2017, 6806, 23161, 79392, 273614, 946981, 3289364, 11460830, 40036253, 140175224, 491756763, 1728190792, 6082921479, 21440851774, 75669652513, 267362335333, 945656056754, 3347973882425, 11863501369311, 42072251661888

Offset

0,3

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, 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):
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}][[1]];
a /@ Range[0, 30] (* Jean-François Alcover, Apr 05 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A008578, A308241, A308273.

Sequence in context: A077834 A325918 A307564 * A328658 A067675 A037512

Adjacent sequences: A308237 A308238 A308239 * A308241 A308242 A308243

Keyword

nonn

Author

Alois P. Heinz, May 16 2019

Status

approved