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A000925
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Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers.
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3
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1, 2, 1, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. Das and A. C. Melissinos, Quantum Mechanics: A Modern Introduction, Gordon and Breach, 1986, p. 47.
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..10000
Index entries for sequences related to sums of squares
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FORMULA
| Coefficient of q^k in (1/4)*(1 + theta_3(0, q))^2.
a(A001481(n))>0; a(A022544(n))=0. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 20 2003
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MATHEMATICA
| a[n_] := (pr = PowersRepresentations[n, 2, 2]; Count[Union[Join[pr, Reverse /@ pr]], {j_ /; j >= 0, k_ /; k >= 0}]); a /@ Range[0, 100] (* From Jean-François Alcover, Apr 05 2011 *)
nn = 100; t = CoefficientList[Series[Sum[x^k^2, {k, 0, Sqrt[nn]}]^2, {x, 0, nn}], x] (* T. D. Noe, Apr 05 2011 *)
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PROG
| (PARI) a(n)=sum(i=0, n, sum(j=0, n, if(i^2+j^2-n, 0, 1)))
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CROSSREFS
| Sequence in context: A025253 A112178 A134663 * A003985 A157237 A065676
Adjacent sequences: A000922 A000923 A000924 * A000926 A000927 A000928
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KEYWORD
| nonn,nice
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AUTHOR
| Jacques Haubrich (jhaubrich(AT)freeler.nl)
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