A000925 Number of ordered ways of writing n as a sum of 2 squares of nonnegative integers.

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

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

Index entries for sequences related to sums of squares

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