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A000075 Number of positive integers <= 2^n of form 2 x^2 + 3 y^2.
(Formerly M1078 N0408)
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

Table of n, a(n) for n=0..35.

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

EXAMPLE

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.

PROG

(PARI) a(n)=if(n<0, 0, sum(k=1, 2^n, 0<sum(y=0, sqrtint(k\3), issquare((k-3*y^2)/2))))

(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

CROSSREFS

Sequence in context: A079488 A054160 A034426 * A048248 A056180 A000076

Adjacent sequences:  A000072 A000073 A000074 * A000076 A000077 A000078

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 26 10:42 EDT 2017. Contains 284111 sequences.