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 A188671 A000145(n) / 8 - (n^5 + 1). 0
 1, 0, -24, -32, 108, 275, -176, -1056, 45, 3157, 1080, -6541, -836, 16839, 2072, -33824, 1188, 67100, 1672, -95883, 19162, 161083, -8208, -224653, 2707, 371325, 67500, -520025, -1188, 870551, 8512, -1082400, 148334, 1419889, 10428, -1588228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS T. C. Hales, The Mathematical Work of the 2010 Fields Medalists, Notices Amer. Math. Soc, 58 (No. 3, Mar 2011), 453-457. See p. 457, Theorem 2. FORMULA 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. a(n) = A000145(n) / 8 - (n^5 + 1). EXAMPLE x - 24*x^3 - 32*x^4 + 108*x^5 + 275*x^6 - 176*x^7 - 1056*x^8 + 45*x^9 + ... PROG (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))} CROSSREFS Cf. A000145. Sequence in context: A269424 A319928 A025102 * A166648 A231468 A179188 Adjacent sequences:  A188668 A188669 A188670 * A188672 A188673 A188674 KEYWORD sign AUTHOR Michael Somos, Apr 11 2011 STATUS approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)