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

Offset

1,5

Comments

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

Links

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Cf. A215933, A215934.

Cf. A000040, A010051.

Sequence in context: A252651 A058485 A204907 * A011326 A154826 A155994

Adjacent sequences: A183165 A183166 A183167 * A183169 A183170 A183171

Keyword

nonn

Author

Zak Seidov, Aug 27 2012

Status

approved