Search: id:A000144
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%I A000144
%S A000144 1,20,180,960,3380,8424,16320,28800,52020,88660,129064,175680,262080,
%T A000144 386920,489600,600960,840500,1137960,1330420,1563840,2050344,2611200,
%U A000144 2986560,3358080,4194240,5318268,5878440,6299520,7862400,9619560
%N A000144 Number of ways of writing n as a sum of 10 squares.
%D A000144 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 121.
%D A000144 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 314.
%D A000144 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his 
               life and work, Chelsea Publishing Company, New York 1959, p. 135 
               section 9.3. MR0106147 (21 #4881)
%H A000144 T. D. Noe, <a href="b000144.txt">Table of n, a(n) for n=0..10000</a>
%H A000144 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 A000144 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%F A000144 Euler transform of period 4 sequence [20, -30, 20, -10, ...]. - Michael 
               Somos Sep 12 2005
%F A000144 Expansion of eta(q^2)^50/(eta(q)eta(q^4))^20 in powers of q. - Michael 
               Somos Sep 12 2005
%F A000144 a(n)=4/5*(A050456(n)+16*A050468(n)+8*A030212(n)) if n>0. - Michael Somos 
               Sepe 12 2005
%p A000144 (sum(x^(m^2),m=-10..10))^10;
%t A000144 Needs["NumberTheory`NumberTheoryFunctions`"]; Table[SumOfSquaresR[10, 
               n], {n, 0, 30}] (*Chandler*)
%o A000144 (PARI) a(n)=if(n<0, 0, polcoeff(sum(k=1,sqrtint(n), 2*x^k^2,1+x*O(x^n))^10, 
               n)) /* Michael Somos Sep 12 2005 */
%Y A000144 Sequence in context: A159538 A091983 A037250 this_sequence A047645 A010936 
               A014806
%Y A000144 Adjacent sequences: A000141 A000142 A000143 this_sequence A000145 A000146 
               A000147
%K A000144 nonn,easy
%O A000144 0,2
%A A000144 N. J. A. Sloane (njas(AT)research.att.com).
%E A000144 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 28 2006

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