Search: id:A000141
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%I A000141
%S A000141 1,12,60,160,252,312,544,960,1020,876,1560,2400,2080,2040,3264,4160,
%T A000141 4092,3480,4380,7200,6552,4608,8160,10560,8224,7812,10200,13120,12480,
%U A000141 10104,14144,19200,16380,11520,17400,24960,18396,16440,24480,27200
%N A000141 Number of ways of writing n as a sum of 6 squares.
%D A000141 S. H. Chan, An elementary proof of Jacobi's six squares theorem, Amer. 
               Math. Monthly, 111 (2004), 806-811.
%D A000141 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 121.
%D A000141 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 314.
%D A000141 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.
%H A000141 T. D. Noe, <a href="b000141.txt">Table of n, a(n) for n=0..10000</a>
%H A000141 H. H. Chan and C. Krattenthaler, <a href="http://arXiv.org/abs/math.NT/
               0407061">Recent progress in the study of representations of integers 
               as sums of squares</a>
%H A000141 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%F A000141 Expansion of theta_3(z)^6.
%F A000141 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]
%p A000141 (sum(x^(m^2),m=-10..10))^6;
%t A000141 Needs["NumberTheory`NumberTheoryFunctions`"]; Table[SumOfSquaresR[6, 
               n], {n, 0, 40}] (*Chandler*)
%Y A000141 Sequence in context: A099830 A158443 A153792 this_sequence A008530 A033486 
               A112415
%Y A000141 Adjacent sequences: A000138 A000139 A000140 this_sequence A000142 A000143 
               A000144
%K A000141 nonn,easy,nice
%O A000141 0,2
%A A000141 N. J. A. Sloane (njas(AT)research.att.com).
%E A000141 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 28 2006
%E A000141 Formula corrected by Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 01 2009

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