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A000152
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Number of ways of writing n as a sum of 16 squares.
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13
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1, 32, 480, 4480, 29152, 140736, 525952, 1580800, 3994080, 8945824, 18626112, 36714624, 67978880, 118156480, 197120256, 321692928, 509145568, 772845120, 1143441760, 1681379200, 2428524096, 3392205824, 4658843520, 6411152640
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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Shi-Chao Chen, Congruences for rs(n), Journal of Number Theory, Volume 130, Issue 9, September 2010, Pages 2028-2032.
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FORMULA
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G.f.: theta_3(0,q)^16, where theta_3 is the 3rd Jacobi theta function. - Ilya Gutkovskiy, Jan 13 2017
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MAPLE
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(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
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MATHEMATICA
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Table[SquaresR[16, n], {n, 0, 23}] (* Ray Chandler, Nov 28 2006 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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