A000074 Number of odd integers <= 2^n of form x^2 + y^2. (Formerly M1077 N0407)

1, 1, 2, 4, 7, 13, 25, 43, 83, 157, 296, 564, 1083, 2077, 4006, 7733, 14968, 29044, 56447, 109864, 214197, 418080, 816907, 1598040, 3129063, 6132106, 12027122, 23606527, 46366165, 91127332, 179207074, 352615528, 694182554, 1367278759

Offset

1,3

Comments

First differences of A000050. - Jean-François Alcover, Mar 19 2014

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Seth A. Troisi, Table of n, a(n) for n = 1..50

Daniel Shanks, The second-order term in the asymptotic expansion of B(x), Math. Comp., 18 (1964), 75-86.

Index entries for sequences related to populations of quadratic forms

Example

a(4)=4 since 2^4=16 and 1=1^2, 5=1^2+2^2, 9=3^2, 13=2^2+3^2.

Prog

(PARI) a(n)=if(n<0, 0, sum(k=1, 2^(n-1), 0<sum(y=0, sqrtint(2*k-1), issquare(2*k-1-y^2))))

Crossrefs

Cf. A000050.

Sequence in context: A102113 A034440 A358334 * A374517 A079958 A224341

Adjacent sequences: A000071 A000072 A000073 * A000075 A000076 A000077

Keyword

nonn

Author

N. J. A. Sloane

Extensions

9 more terms from Sean A. Irvine, Sep 14 2009

Status

approved