A330316 a(n) = r(n)*r(n+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.

1, 4, 0, 0, 8, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 16, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 24

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..100.

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.

Mathematica

Times@@#/4&/@Partition[SquaresR[2, Range[0, 110]], 2, 1] (* Harvey P. Dale, May 30 2020 *)

Crossrefs

Cf. A004018, A330315, A330317, A330318.

Sequence in context: A321433 A016678 A055028 * A028591 A048728 A002915

Adjacent sequences: A330313 A330314 A330315 * A330317 A330318 A330319

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2019

Status

approved