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A000076
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Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.
(Formerly M1079 N0409)
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1
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0, 0, 1, 2, 4, 7, 14, 24, 43, 82, 149, 284, 534, 1015, 1937, 3713, 7136, 13759, 26597, 51537, 100045, 194586, 378987, 739161, 1443465, 2821923, 5522689
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| 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
| Index entries for sequences related to populations of quadratic forms
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EXAMPLE
| a(4)=4 since 2^4=16 and 4=4*1^2, 5=5*1^2, 13=4*1^2+4*1*1+5*1^2, 16=4*2^2.
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PROG
| (PARI) a(n)=if(n<0, 0, sum(k=1, 2^n, 0<sum(j=0, sqrtint(k)\2, issquare(k-4*j^2)&(k-j)%2==0)))
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CROSSREFS
| Sequence in context: A000075 A048248 A056180 * A054169 A065491 A072810
Adjacent sequences: A000073 A000074 A000075 * A000077 A000078 A000079
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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