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%I #21 Jul 19 2015 05:44:59
%S 1,0,-24,-32,108,275,-176,-1056,45,3157,1080,-6541,-836,16839,2072,
%T -33824,1188,67100,1672,-95883,19162,161083,-8208,-224653,2707,371325,
%U 67500,-520025,-1188,870551,8512,-1082400,148334,1419889,10428,-1588228
%N A000145(n) / 8 - (n^5 + 1).
%C Theorem 2 in the Hales reference defines t_p = (n_p - 8(p^5 + 1)) / (32 p^(5/2)) where n_p is the number of ways to express p as a sum of 12 squares.
%H T. C. Hales, <a href="http://www.ams.org/notices/201103/rtx110300453p.pdf">The Mathematical Work of the 2010 Fields Medalists</a>, Notices Amer. Math. Soc, 58 (No. 3, Mar 2011), 453-457. See p. 457, Theorem 2.
%F G.f.: ((Sum_{k} x^k^2)^12 - 1) / 8 - (2*x + 21*x^2 + 76*x^3 + 16*x^4 + 6*x^5 - x^6) / (1 - x)^6.
%F a(n) = A000145(n) / 8 - (n^5 + 1).
%e x - 24*x^3 - 32*x^4 + 108*x^5 + 275*x^6 - 176*x^7 - 1056*x^8 + 45*x^9 + ...
%o (PARI) {a(n) = if( n<1, 0, polcoeff( sum( k = 1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^12, n) / 8 - (n^5 + 1))}
%Y Cf. A000145.
%K sign
%O 1,3
%A _Michael Somos_, Apr 11 2011