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EXAMPLE
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There are a(4) = 24 solutions (w,x,y,z) of 4^2 = w^2 + x^2 + y^2 + z^2:
(2,2,2,2), (-2,-2,-2,-2), 6 permutations of (2,2,-2,-2),
4 permutations of (2,2,2,-2), 4 permutations of (2,-2,-2,-2),
4 permutations of (4,0,0,0), and 4 permutations of (-4,0,0,0).
To illustrate a(n) = the coefficient of x^(n^2) in theta_3(x)^n, where
theta_3(x) = 1 + 2*x + 2*x^4 + 2*x^9 + 2*x^16 + 2*x^25 + 2*x^36 + 2*x^49 +...,
form a table of coefficients of x^k in theta_3(x)^n, n>=0, like so:
n\k:0..1...2...3...4...5...6...7...8...9..10..11..12..13..14..15..16....
0:[(1),0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...];
1: [1,(2), 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2,...];
2: [1, 4, 4, 0, (4), 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4,...];
3: [1, 6, 12, 8, 6, 24, 24, 0, 12,(30),24, 24, 8, 24, 48, 0, 6,...];
4: [1, 8, 24, 32, 24, 48, 96, 64, 24,104,144, 96, 96,112,192,192,(24),...];
5: [1,10, 40, 80, 90,112,240,320,200,250,560,560,400,560,800,960,730,...];
then the coefficients in parenthesis form the initial terms of this sequence.
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