A330318 a(n) = Sum_{i=0..n} r(i)*r(i+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.

1, 5, 5, 5, 13, 13, 13, 13, 17, 25, 25, 25, 25, 25, 25, 25, 33, 41, 41, 41, 41, 41, 41, 41, 41, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 73, 73, 73, 73, 89, 89, 89, 89, 89, 89, 89, 89, 89, 101, 101, 101, 117, 117, 117, 117, 117, 117, 117, 117, 117, 117

Offset: 0

Author

N. J. A. Sloane, Dec 11 2019

Keywords

• nonn

References

• H. Iwaniec. Spectral methods of automorphic forms, volume 53 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2002.

Links

• Fernando Chamizo, Correlated sums of r(n), J. Math. Soc. Japan, 51(1):237-252, 1999.
• Fernando Chamizo, and Roberto J. Miatello, Sums of squares in real quadratic fields and Hilbert modular groups, arXiv preprint arXiv:1812.10725 [math.NT], 2018.

Crossrefs

Cf. A004018, A330315, A330317.

Partial sums of A330316.