A308274 Total number of nodes summed over all lattice paths from (0,0) to (n,n) that do not go above the diagonal x=y and consist of steps (h,v) with h, v prime or one.

1, 2, 5, 15, 47, 147, 469, 1531, 5076, 17014, 57537, 196043, 671980, 2314592, 8005266, 27784114, 96720440, 337572161, 1180869043, 4139120434, 14534125630, 51116699820, 180036470572, 634925138580, 2241803318605, 7923931456994, 28035799832528, 99284104334614

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)) and
      (x-h<=y-v), b(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]) &&
     x-h <= y-v, b[{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, A308241, A308273.

Sequence in context: A346521 A148362 A143094 * A058495 A287275 A151280

Adjacent sequences: A308271 A308272 A308273 * A308275 A308276 A308277

Keyword

nonn

Author

Alois P. Heinz, May 17 2019

Status

approved