A317683 Number of partitions of n into a prime and two distinct positive squares.

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 2, 2, 1, 2, 1, 2, 1, 3, 2, 3, 1, 1, 3, 4, 2, 3, 3, 3, 3, 3, 0, 6, 3, 1, 5, 3, 2, 6, 4, 4, 3, 4, 4, 7, 2, 3, 4, 5, 4, 6, 4, 5, 7, 6, 2, 7, 3, 2, 9, 6, 3, 7, 5, 6, 6, 7, 6, 9, 4, 4, 5, 9, 5, 9, 5, 4

Offset: 0

Author

R. J. Mathar, Michel Marcus, Aug 04 2018

Keywords

• nonn
• easy

Comments

As in A025441, the two squares must be distinct and positive.

Examples

			a(12)=2 counts 12 = 7 +1^2 +2^2 = 2 + 1^2 +3^2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A025441, A317682 - A317685.

Programs

Maple

A317683 := proc(n)
    a := 0 ;
    p := 2;
    while p <= n do
        a := a+A025441(n-p);
        p := nextprime(p) ;
    end do:
    a ;
end proc:

Mathematica

p2sQ[n_]:=Length[Union[n]]==3&&Count[n,?(IntegerQ[Sqrt[#]]&)]==2&&Count[ n,?(PrimeQ[#]&)]==1; Table[Count[IntegerPartitions[n,{3}],?p2sQ],{n,0,80}] (* _Harvey P. Dale, Sep 21 2019 *)

Formula

a(n) = Sum_{primes p} A025441(n-p).