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A243940
Number of partitions of n^2 into exactly 4 prime numbers.
2
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
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
KEYWORD
nonn
AUTHOR
Olivier Gérard, Jun 15 2014
STATUS
approved