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Search: id:A000075
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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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+0
1
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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
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
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LINKS
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Index entries for sequences related to populations of quadratic forms
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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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PROGRAM
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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))))
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CROSSREFS
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Adjacent sequences: A000072 A000073 A000074 this_sequence A000076 A000077 A000078
Sequence in context: A079488 A054160 A034426 this_sequence A048248 A056180 A000076
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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