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Search: id:A066535
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| A066535 |
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Number of ways of writing n as a sum of n squares. |
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+0
3
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| 1, 2, 4, 8, 24, 112, 544, 2368, 9328, 34802, 129064, 491768, 1938336, 7801744, 31553344, 127083328, 509145568, 2035437440, 8148505828, 32728127192, 131880275664, 532597541344, 2153312518240, 8710505815360, 35250721087168
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) equals the coefficient of x^n in the n-th power of Jacobi theta_3(x) where theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2). [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009]
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EXAMPLE
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There are a(3)=8 solutions (x,y,z) of 3=x^2+y^2+z^2: (1,1,1), (-1,-1, -1), 3 permutations of (1,1,-1) and 3 permutations of (1,-1,-1).
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MATHEMATICA
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a[ n_ ] := SumOfSquaresR[ n, n ] (* First load package NumberTheory`NumberTheoryFunctions` *)
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PROGRAM
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(PARI) {a(n)=local(THETA3=1+2*sum(k=1, sqrtint(n), x^(k^2))+x*O(x^n)); polcoeff(THETA3^n, n)} /* Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009 */
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CROSSREFS
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Cf. A004018, A005875, A000118, A066536.
Cf. A122141, A166952 [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009]
Sequence in context: A065654 A002908 A004528 this_sequence A000643 A112285 A037170
Adjacent sequences: A066532 A066533 A066534 this_sequence A066536 A066537 A066538
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KEYWORD
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nonn
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AUTHOR
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Peter Bertok (peter(AT)bertok.com), Jan 07 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 12, 2002.
a(0) added by Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2009
Edited by R. J. Mathar, Oct 29 2009
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