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A000145
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Number of ways of writing n as a sum of 12 squares.
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4
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1, 24, 264, 1760, 7944, 25872, 64416, 133056, 253704, 472760, 825264, 1297056, 1938336, 2963664, 4437312, 6091584, 8118024, 11368368, 15653352, 19822176, 24832944, 32826112, 42517728, 51425088, 61903776, 78146664, 98021616
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Apparently 8 | a(n). - Alexander R. Povolotsky, Oct 1 2011
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REFERENCES
| E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 314.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10000
Index entries for sequences related to sums of squares
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FORMULA
| Expansion of eta(q^2)^60 / (eta(q) * eta(q^4))^24 in powers of q.
Euler transform of period 4 sequence [24, -36, 24, -12, ...]. - Michael Somos Sep 21 2005
G.f.: (Sum_k x^k^2)^12 = theta_3(q)^12.
a(n) = A029751(n) + 16 * A000735(n). - Michael Somos Sep 21 2005
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EXAMPLE
| 1 + 24*x + 264*x^2 + 1760*x^3 + 7944*x^4 + 25872*x^5 + 64416*x^6 + 133056*x^7 + ...
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MAPLE
| (sum(x^(m^2), m=-10..10))^12; # gives g.f. for first 100 terms
coeff(((sum(x^(m^2), m=-10..10)))^12, x, 1...100)[from Alexander R. Povolotsky Oct 1 2011]
t1:=(sum(x^(m^2), m=-n..n))^12; t2:=series(t1, x, n+1); t2[n+1];
[from N. J. A. Sloane Oct 1 2011]
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( sum( k=1, sqrtint(n), 2 * x^k^2, 1 + x * O(x^n))^12, n))} /* Michael Somos Sep 21 2005 */
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CROSSREFS
| Cf. A000735, A029751.
Sequence in context: A076847 A009175 A187380 * A126904 A001413 A022065
Adjacent sequences: A000142 A000143 A000144 * A000146 A000147 A000148
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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