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%I #14 May 21 2024 09:41:07
%S 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,
%T 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,
%U 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
%N 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.
%D H. Iwaniec. Spectral methods of automorphic forms, volume 53 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2002.
%H Fernando Chamizo, <a href="https://doi.org/10.2969/jmsj/05110237">Correlated sums of r(n)</a>, J. Math. Soc. Japan, 51(1):237-252, 1999.
%H Fernando Chamizo, and Roberto J. Miatello, <a href="https://arxiv.org/abs/1812.10725">Sums of squares in real quadratic fields and Hilbert modular groups</a>, arXiv preprint arXiv:1812.10725 [math.NT], 2018.
%t Times@@#/4&/@Partition[SquaresR[2,Range[0,110]],2,1] (* _Harvey P. Dale_, May 30 2020 *)
%Y Cf. A004018, A330315, A330317, A330318.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Dec 11 2019
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