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%I #16 Dec 06 2018 11:33:37
%S 1,0,3,0,0,0,5,0,2,0,1,0,1,0,2,0,2,1,0,4,1,2,0,0,7,0,2,2,0,1,0,4,0,0,
%T 0,0,0,5,0,0,0,0,0,2,0,0,0,0,0,2,0,2,0,0,1,0,0,1,0,2,0,0,0,1,2,0,2,0,
%U 0,0,0,0,2,1,0,1,0,0,0,0,0,0,2,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0
%N The number of numbers k > n such that Sum_{i=n..k} i^2 is a square.
%C It is an old result (see Watson) that for n=1 the only k>n is k=24. Bremner, Stroeker, and Tzanakis compute the k for n <= 100 by solving elliptic curves. This sequence lists the number of k for each n; the values of k are in A184763. Sequence A180442 lists the n for which a(n) is nonzero.
%H A. Bremner, R. J. Stroeker, N. Tzanakis, <a href="https://doi.org/10.1006/jnth.1997.2040">On Sums of Consecutive Squares</a>, J. Number Theory 62 (1997), 39-70.
%H G. N. Watson, <a href="http://archive.org/stream/messengerofmathe4849cambuoft#page/n9/mode/2up">The problem of the square pyramid</a>, Messenger of Mathematics 48 (1918), pp. 1-22.
%Y Cf. A075404, A075405, A075406.
%K nonn,hard
%O 1,3
%A _T. D. Noe_, Jan 21 2011
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