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

1, 22, 220, 1320, 5302, 15224, 33528, 63360, 116380, 209550, 339064, 491768, 719400, 1095160, 1538416, 1964160, 2624182, 3696880, 4763220, 5686648, 7217144, 9528816, 11676280, 13495680, 16317048, 20787470, 25022184, 27785120, 32503680

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• 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.

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Shi-Chao Chen, Congruences for rs(n), Journal of Number Theory, Volume 130, Issue 9, September 2010, Pages 2028-2032.
• Shaun Cooper, On the number of representations of certain integers as sums of 11 or 13 squares, J. Number Theory 103 (2) (2003) 135-162
• Index entries for sequences related to sums of squares

Crossrefs

Row d=11 of A122141 and of A319574, 11th column of A286815.

Cf. A022042.

Programs

Maple

(sum(x^(m^2),m=-10..10))^11;
# Alternative:
A008453list := proc(len) series(JacobiTheta3(0, x)^11, x, len+1);
seq(coeff(%, x, j), j=0..len-1) end: A008453list(29); # Peter Luschny, Oct 02 2018

Mathematica

Table[SquaresR[11, n], {n, 0, 28}] (* Ray Chandler, Nov 28 2006 *)

Formula

G.f.: theta_3(0,q)^11, where theta_3 is the 3rd Jacobi theta function. - Ilya Gutkovskiy, Jan 13 2017

a(n) = (22/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - Seiichi Manyama, May 27 2017

Extensions

Extended by Ray Chandler, Nov 28 2006