A000067 Number of positive integers <= 2^n of form x^2 + 2 y^2. (Formerly M1016 N0382)

1, 2, 4, 6, 10, 18, 33, 60, 111, 205, 385, 725, 1374, 2610, 4993, 9578, 18426, 35568, 68806, 133411, 259145, 504222, 982538, 1917190, 3745385, 7324822, 14339072, 28095711, 55095559, 108124461, 212342327, 417283564, 820520378, 1614331755, 3177789615, 6258525127

Offset

0,2

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 = 0..58

D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.

Seth A. Troisi, C++ program

Index entries for sequences related to populations of quadratic forms

Example

a(3)=6 since 2^3=8 and 1=1^2, 2=2*1^2, 3=1^2+2*1^2, 4=2^2, 6=2^2+2*1^2, 8=2*2^2.

Prog

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

Crossrefs

Sequence in context: A232582 A018074 A288465 * A133140 A349592 A026680

Adjacent sequences: A000064 A000065 A000066 * A000068 A000069 A000070

Keyword

nonn

Author

N. J. A. Sloane

Status

approved