cp's OEIS Frontend

A008453 Number of ways of writing n as a sum of 11 squares.

%I A008453 #40 Dec 27 2021 21:26:40
%S A008453 1,22,220,1320,5302,15224,33528,63360,116380,209550,339064,491768,
%T A008453 719400,1095160,1538416,1964160,2624182,3696880,4763220,5686648,
%U A008453 7217144,9528816,11676280,13495680,16317048,20787470,25022184,27785120,32503680
%N A008453 Number of ways of writing n as a sum of 11 squares.
%D A008453 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.
%D A008453 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 314.
%H A008453 T. D. Noe, <a href="/A008453/b008453.txt">Table of n, a(n) for n = 0..10000</a>
%H A008453 Shi-Chao Chen, <a href="http://dx.doi.org/10.1016/j.jnt.2010.01.011">Congruences for rs(n)</a>, Journal of Number Theory, Volume 130, Issue 9, September 2010, Pages 2028-2032.
%H A008453 Shaun Cooper, <a href="http://dx.doi.org/10.1016/j.jnt.2003.06.001">On the number of representations of certain integers as sums of 11 or 13 squares</a>, J. Number Theory 103 (2) (2003) 135-162
%H A008453 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A008453 G.f.: theta_3(0,q)^11, where theta_3 is the 3rd Jacobi theta function. - _Ilya Gutkovskiy_, Jan 13 2017
%F A008453 a(n) = (22/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, May 27 2017
%p A008453 (sum(x^(m^2),m=-10..10))^11;
%p A008453 # Alternative:
%p A008453 A008453list := proc(len) series(JacobiTheta3(0, x)^11, x, len+1);
%p A008453 seq(coeff(%, x, j), j=0..len-1) end: A008453list(29); # _Peter Luschny_, Oct 02 2018
%t A008453 Table[SquaresR[11, n], {n, 0, 28}] (* _Ray Chandler_, Nov 28 2006 *)
%Y A008453 Row d=11 of A122141 and of A319574, 11th column of A286815.
%Y A008453 Cf. A022042.
%K A008453 nonn
%O A008453 0,2
%A A008453 _N. J. A. Sloane_
%E A008453 Extended by _Ray Chandler_, Nov 28 2006