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 A000925 Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers. 11
 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; text; internal format)
 OFFSET 0,2 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. LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 FORMULA Coefficient of q^k in (1/4)*(1 + theta_3(0, q))^2. a(A001481(n))>0; a(A022544(n))=0. - Benoit Cloitre, Apr 20 2003 MATHEMATICA a[n_] := (pr = PowersRepresentations[n, 2, 2]; Count[Union[Join[pr, Reverse /@ pr]], {j_ /; j >= 0, k_ /; k >= 0}]); a /@ Range[0, 100] (* 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 *) SquareQ[n_] := IntegerQ[Sqrt[n]]; Table[Count[FrobeniusSolve[{1, 1}, n], {__?SquareQ}], {n, 0, 100}] (* Robert G. Wilson v, Apr 15 2017 *) PROG (PARI) a(n)=sum(i=0, n, sum(j=0, n, if(i^2+j^2-n, 0, 1))) (Haskell) a000925 n = sum \$ map (a010052 . (n -)) \$ takeWhile (<= n) a000290_list -- Reinhard Zumkeller, Sep 14 2014 CROSSREFS Cf. A000290, A010052, A000161, A247367. Sequence in context: A284575 A112178 A134663 * A258279 A258292 A003985 Adjacent sequences:  A000922 A000923 A000924 * A000926 A000927 A000928 KEYWORD nonn,nice AUTHOR Jacques Haubrich (jhaubrich(AT)freeler.nl) STATUS approved

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