A000075 Number of positive integers <= 2^n of form 2 x^2 + 3 y^2.

0, 1, 2, 4, 7, 14, 23, 42, 76, 139, 258, 482, 907, 1717, 3269, 6257, 12020, 23171, 44762, 86683, 168233, 327053, 636837, 1241723, 2424228, 4738426, 9271299, 18157441, 35591647, 69820626, 137068908, 269270450, 529312241, 1041093048, 2048825748, 4034059456

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			a(3)=4 since 2^3=8 and 2=2*1^2, 3=3*1^2, 5=2*1^2+3*1^2, 8=2*2^2.
		

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

• D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
• Index entries for sequences related to populations of quadratic forms

Crossrefs

Cf. A002480.

Programs

PARI

a(n)=if(n<0,0,sum(k=1,2^n,0
				

Python

import math
def A000075(n):
    return len(set([2*x**2+3*y**2 for x in range(1+int(math.floor(2**((n-1)/2)))) for y in range(1+int(math.floor(math.sqrt((2**n-2*x**2)/3)))) if 0 < 2*x**2+3*y**2 <= 2**n]))
# Chai Wah Wu, Aug 20 2014