A183168 Number of partitions of n^2 into three distinct primes.

0, 0, 0, 1, 2, 3, 8, 2, 17, 3, 41, 7, 61, 6, 69, 8, 152, 11, 216, 6, 204, 10, 383, 16, 464, 14, 447, 14, 791, 18, 978, 18, 822, 18, 1302, 25, 1684, 27, 1387, 24, 2347, 28, 2726, 27, 2012, 34, 3620, 31, 4005, 32, 3218, 44, 5274, 44, 5461, 36, 4538, 43, 7429, 58

Offset: 1

Author

Zak Seidov, Aug 27 2012

Keywords

• nonn

Comments

For n>3, odd n have (many) more partitions than even n.

Examples

			a(4)=1 because 16=2+3+11,
a(6)=3 because 36=2+3+31=2+5+29=2+11+13.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..200

Crossrefs

Subsequence of A125688: a(n) = A125688(n^2).

Cf. A215933, A215934.

Cf. A000040, A010051.

Cf. A000607.

Programs

Haskell

a183168 n = z (drop (fromInteger (mod n 2)) a000040_list) (n ^ 2) 3 where
   z _      m 1 = if m <= 0 then 0 else a010051 m
   z (p:ps) m c = if m <= 2*p then 0 else z ps (m - p) (c - 1) + z ps m c
-- Reinhard Zumkeller, Aug 28 2012

Mathematica

Table[Count[Union/@IntegerPartitions[n^2,{3}],?(Length[#]==3&&AllTrue[ #, PrimeQ]&)],{n,60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale, May 02 2018 *)

PARI

a(n)=my(s);n*=n;forprime(p=n\3,n-4,forprime(q=(n-p)\2+1,min(n-p,p-1),if(isprime(n-p-q),s++)));s \\ Charles R Greathouse IV, Aug 27 2012