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

%I A341459 #14 May 02 2022 02:58:42
%S A341459 1,0,1,4,22,241,2696,35218,529888,8998419,169486964,3496417024,
%T A341459 78344008779,1891733424205,48923563968087,1347813311456319,
%U A341459 39371345548420060,1214570579814316742,39430967625404799740,1343040950675651131103,47862610677098010505554
%N A341459 Number of compositions of n^2 into n prime parts.
%H A341459 Alois P. Heinz, <a href="/A341459/b341459.txt">Table of n, a(n) for n = 0..100</a>
%F A341459 a(n) = A121303(n^2,n).
%e A341459 a(3) = 4: 333, 225, 252, 522.
%p A341459 b:= proc(n, t) option remember;
%p A341459       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341459       `if`(isprime(j), b(n-j, t-1), 0), j=1..n)))
%p A341459     end:
%p A341459 a:= n-> b(n^2, n):
%p A341459 seq(a(n), n=0..22);
%t A341459 b[n_, t_] := b[n, t] =
%t A341459      If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
%t A341459      If[PrimeQ[j], b[n-j, t-1], 0], {j, 1, n}]]];
%t A341459 a[n_] := b[n^2, n];
%t A341459 Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, May 02 2022, after _Alois P. Heinz_ *)
%Y A341459 Cf. A023360, A035026, A121303, A299168.
%K A341459 nonn
%O A341459 0,4
%A A341459 _Alois P. Heinz_, Feb 12 2021