A243940 Number of partitions of n^2 into exactly 4 prime numbers.

0, 0, 1, 3, 5, 15, 13, 50, 24, 126, 50, 258, 78, 508, 115, 899, 176, 1562, 240, 2383, 299, 3616, 440, 5733, 547, 7585, 664, 10705, 863, 16259, 1033, 19591, 1234, 25943, 1566, 37879, 1860, 43405, 1976, 55700, 2529, 78989, 2942, 86261, 3162, 106212, 3867, 148771

Offset: 1

Author

Olivier Gérard, Jun 15 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Programs

Maple

with(numtheory):
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(i<1 or t<1, 0, b(n, i-1, t) +(p-> `if`(p>n, 0,
         b(n-p, i, t-1)))(ithprime(i))))
    end:
a:= n-> b(n^2, pi(n^2), 4):
seq(a(n), n=1..40);  # Alois P. Heinz, Jun 15 2014

Mathematica

$RecursionLimit = 1000; b[n_, i_, t_] :=  b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + Function[{p}, If[p > n, 0, b[n - p, i, t - 1]]][Prime[i]]]]; a[n_] := b[n^2, PrimePi[n^2], 4]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 15 2015, after Alois P. Heinz *)