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

1,4

Links

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

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 *)

Crossrefs

Sequence in context: A111869 A093015 A371450 * A066420 A102582 A351296

Adjacent sequences: A243937 A243938 A243939 * A243941 A243942 A243943

Keyword

nonn

Author

Olivier Gérard, Jun 15 2014

Status

approved