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Search: id:A000145
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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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+0
3
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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
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OFFSET
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0,2
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COMMENT
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a(n)=A029751(n)+16*A000735(n). - Michael Somos Sep 21 2005
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REFERENCES
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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
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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
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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.: (Product_{k>0} (1-x^k))^12 = theta_3(q)^12.
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MAPLE
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(sum(x^(m^2), m=-10..10))^12;
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PROGRAM
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(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
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Sequence in context: A051828 A076847 A009175 this_sequence A126904 A001413 A022065
Adjacent sequences: A000142 A000143 A000144 this_sequence A000146 A000147 A000148
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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