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Search: id:A066536
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| A066536 |
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Number of ways of writing n as a sum of n+1 squares. |
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+0
3
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| 1, 4, 12, 32, 90, 312, 1288, 5504, 22608, 88660, 339064, 1297056, 5043376, 19975256, 80027280, 321692928, 1291650786, 5177295432, 20748447108, 83279292960, 335056780464, 1351064867328, 5456890474248, 22063059606912
(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+1)-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 26 2009]
a(n) is divisible by n+1: a(n)/(n+1) = A166952(n) for n>=0. [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009]
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EXAMPLE
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There are a(2)=12 solutions (x,y,z) of 2=x^2+y^2+z^2: 3 permutations of (1,1,0), 3 permutations of (-1,-1,0) and 6 permutations of (1, -1,0).
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MATHEMATICA
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a[ n_ ] := SumOfSquaresR[ n+1, 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+1), n)} /* Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009*/
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CROSSREFS
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Cf. A004018, A005875, A000118, A066535.
Cf. A122141, A166952 [Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2009]
Sequence in context: A135248 A120369 A001665 this_sequence A104747 A070050 A027941
Adjacent sequences: A066533 A066534 A066535 this_sequence A066537 A066538 A066539
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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 26 2009
Edited by R. J. Mathar, Oct 29 2009
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