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Search: id:A000141
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| A000141 |
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Number of ways of writing n as a sum of 6 squares. |
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+0
8
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| 1, 12, 60, 160, 252, 312, 544, 960, 1020, 876, 1560, 2400, 2080, 2040, 3264, 4160, 4092, 3480, 4380, 7200, 6552, 4608, 8160, 10560, 8224, 7812, 10200, 13120, 12480, 10104, 14144, 19200, 16380, 11520, 17400, 24960, 18396, 16440, 24480, 27200
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. H. Chan, An elementary proof of Jacobi's six squares theorem, Amer. Math. Monthly, 111 (2004), 806-811.
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.
S. C. Milne, Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions and Schur functions, Ramanujan J., 6 (2002), 7-149.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares
Index entries for sequences related to sums of squares
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FORMULA
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Expansion of theta_3(z)^6.
a(n) = 4( Sum_{ d|n, d ==3 mod 4} d^2 - Sum_{ d|n, d ==1 mod 4} d^2 ) + 16( Sum_{ d|n, n/d ==1 mod 4} d^2 - Sum_{ d|n, n/d ==3 mod 4} d^2 ) [Jacobi]
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MAPLE
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(sum(x^(m^2), m=-10..10))^6;
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; Table[SumOfSquaresR[6, n], {n, 0, 40}] (*Chandler*)
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CROSSREFS
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Sequence in context: A099830 A158443 A153792 this_sequence A008530 A033486 A112415
Adjacent sequences: A000138 A000139 A000140 this_sequence A000142 A000143 A000144
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 28 2006
Formula corrected by Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 01 2009
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