A308241 Total number of nodes summed over all lattice paths from (0,0) to (n,n) that consist of steps (h,v) with h, v prime or one.

1, 2, 5, 18, 68, 244, 880, 3228, 11905, 43966, 162498, 600984, 2222776, 8218022, 30368708, 112162230, 414006377, 1527214022, 5630258676, 20744334800, 76387507859, 281129870088, 1034103899368, 3801934437930, 13971364199298, 51318841190524, 188420580871859

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

Cf. A000040, A008578, A308240, A308274.

Sequence in context: A150023 A150024 A150025 * A363061 A288910 A249062

Adjacent sequences: A308238 A308239 A308240 * A308242 A308243 A308244

Keyword

nonn

Author

Alois P. Heinz, May 16 2019

Status

approved