A341459 Number of compositions of n^2 into n prime parts.

1, 0, 1, 4, 22, 241, 2696, 35218, 529888, 8998419, 169486964, 3496417024, 78344008779, 1891733424205, 48923563968087, 1347813311456319, 39371345548420060, 1214570579814316742, 39430967625404799740, 1343040950675651131103, 47862610677098010505554

Offset: 0

Author

Alois P. Heinz, Feb 12 2021

Keywords

• nonn

Examples

			a(3) = 4: 333, 225, 252, 522.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A023360, A035026, A121303, A299168.

Programs

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n^2, n):
seq(a(n), n=0..22);

Mathematica

b[n_, t_] := b[n, t] =
     If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
     If[PrimeQ[j], b[n-j, t-1], 0], {j, 1, n}]]];
a[n_] := b[n^2, n];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, May 02 2022, after Alois P. Heinz *)

Formula

a(n) = A121303(n^2,n).