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A317684 Number of partitions of n into a prime and two squares. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..80.

C. Hooley, On the representation of a number as the sum of two squares and a prime, Acta Mathem. 97 (1957) 189-210

FORMULA

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

EXAMPLE

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.

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:

CROSSREFS

Cf. A000161, A317682-A317685.

Sequence in context: A304817 A242802 A277561 * A127973 A300654 A023157

Adjacent sequences:  A317681 A317682 A317683 * A317685 A317686 A317687

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)