OFFSET
0,2
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 314.
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 107.
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.
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.
FORMULA
G.f.: theta_3(0,q)^16, where theta_3 is the 3rd Jacobi theta function. - Ilya Gutkovskiy, Jan 13 2017
a(n) = (32/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - Seiichi Manyama, May 27 2017
MAPLE
(sum(x^(m^2), m=-10..10))^16;
# Alternative:
A000152list := proc(len) series(JacobiTheta3(0, x)^16, x, len+1);
seq(coeff(%, x, j), j=0..len-1) end: A000152list(24); # Peter Luschny, Oct 02 2018
MATHEMATICA
Table[SquaresR[16, n], {n, 0, 23}] (* Ray Chandler, Nov 28 2006 *)
CoefficientList[EllipticTheta[3, 0, x]^16 + O[x]^24, x] (* Jean-François Alcover, Jul 06 2017 *)
PROG
(PARI) first(n)=my(x='x); x+=O(x^(n+1)); Vec((2*sum(k=1, sqrtint(n), x^k^2) + 1)^16) \\ Charles R Greathouse IV, Jul 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended by Ray Chandler, Nov 28 2006
STATUS
approved