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Search: id:A000072
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| A000072 |
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Number of positive integers <= 2^n of form x^2 + 4 y^2.
(Formerly M1063 N0400)
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+0
3
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| 1, 1, 2, 4, 7, 12, 22, 41, 72, 137, 254, 476, 901, 1716, 3274, 6286, 12090, 23331, 45140, 87511, 169972, 330752, 644499, 1257523, 2456736, 4804666, 9405749, 18429828, 36141339, 70928099, 139295793, 273741700, 538277486, 1059051586, 2084763319, 4105924366
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
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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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 1=1^2, 4=2^2=4*1^2, 5=1^2+4*1^2, 8=2^2+1*1^2.
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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\4), issquare(k-4*y^2))))
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CROSSREFS
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Sequence in context: A026713 A002573 A064492 this_sequence A018179 A127542 A023432
Adjacent sequences: A000069 A000070 A000071 this_sequence A000073 A000074 A000075
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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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