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Search: id:A000067
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| A000067 |
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Number of positive integers <= 2^n of form x^2 + 2 y^2.
(Formerly M1016 N0382)
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+0
1
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| 1, 2, 4, 6, 10, 18, 33, 60, 111, 205, 385, 725, 1374, 2610, 4993, 9578, 18426, 35568, 68806, 133411, 259145, 504222, 982538, 1917190, 3745385, 7324822, 14339072, 28095711, 55095559, 108124461, 212342327, 417283564, 820520378, 1614331755, 3177789615, 6258525127
(list; graph; listen)
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OFFSET
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0,2
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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)=6 since 2^3=8 and 1=1^2, 2=2*1^2, 3=1^2+2*1^2, 4=2^2, 6=2^2+2*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\2), issquare(k-2*y^2))))
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CROSSREFS
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Sequence in context: A098197 A102477 A018074 this_sequence A133140 A026680 A164141
Adjacent sequences: A000064 A000065 A000066 this_sequence A000068 A000069 A000070
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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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