A317684 Number of partitions of n into a prime and two squares.

0, 0, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 2, 5, 3, 3, 4, 5, 5, 6, 4, 6, 4, 4, 2, 7, 6, 5, 5, 7, 6, 6, 4, 4, 7, 7, 5, 10, 4, 6, 8, 8, 6, 8, 5, 9, 9, 7, 4, 8, 8, 8, 9, 10, 8, 10, 6, 6, 9, 9, 6, 14, 6, 6, 10, 10, 10, 12, 8, 10, 12, 9, 6, 12, 10, 11, 11, 12, 7

Offset: 0

Author

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

Keywords

• nonn
• look
• easy

Comments

As in A000161, the squares may be zero and do not need to be distinct.

Examples

			a(11) = 4 counts 11 = 11+0^2+0^2 = 7+0^2+2^2 = 2+0^2+3^2 = 3+2^2+2^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• C. Hooley, On the representation of a number as the sum of two squares and a prime, Acta Mathem. 97 (1957) 189-210

Crossrefs

Cf. A000161, A317682-A317685.

Programs

Maple

A317684 := proc(n)
    a := 0 ;
    p := 2;
    while p <= n do
        a := a+A000161(n-p);
        p := nextprime(p) ;
    end do:
    a ;
end proc:

Formula

a(n) = Sum_{primes p} A000161(n-p).