Search: id:A000145
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%I A000145
%S A000145 1,24,264,1760,7944,25872,64416,133056,253704,472760,825264,1297056,
%T A000145 1938336,2963664,4437312,6091584,8118024,11368368,15653352,19822176,
%U A000145 24832944,32826112,42517728,51425088,61903776,78146664,98021616
%N A000145 Number of ways of writing n as a sum of 12 squares.
%C A000145 a(n)=A029751(n)+16*A000735(n). - Michael Somos Sep 21 2005
%D A000145 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 121.
%D A000145 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 314.
%H A000145 T. D. Noe, <a href="b000145.txt">Table of n, a(n) for n=0..10000</a>
%H A000145 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%F A000145 Expansion of eta(q^2)^60/(eta(q)eta(q^4))^24 in powers of q.
%F A000145 Euler transform of period 4 sequence [24, -36, 24, -12, ...]. - Michael 
               Somos Sep 21 2005
%F A000145 G.f.: (Product_{k>0} (1-x^k))^12 = theta_3(q)^12.
%p A000145 (sum(x^(m^2),m=-10..10))^12;
%o A000145 (PARI) a(n)=if(n<0, 0, polcoeff(sum(k=1,sqrtint(n),2*x^k^2,1+x*O(x^n))^12,
               n)) /* Michael Somos Sep 21 2005 */
%Y A000145 Sequence in context: A051828 A076847 A009175 this_sequence A126904 A001413 
               A022065
%Y A000145 Adjacent sequences: A000142 A000143 A000144 this_sequence A000146 A000147 
               A000148
%K A000145 nonn,easy
%O A000145 0,2
%A A000145 N. J. A. Sloane (njas(AT)research.att.com).

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