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A000925 Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers. 19
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
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
Sequence in context: A284575 A112178 A134663 * A258279 A258292 A003985
KEYWORD
nonn,nice
AUTHOR
Jacques Haubrich (jhaubrich(AT)freeler.nl)
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)