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A000075
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Number of positive integers <= 2^n of form 2 x^2 + 3 y^2.
(Formerly M1078 N0408)
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2
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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
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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]))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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