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A000021
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Number of positive integers <= 2^n of form x^2 + 12 y^2.
(Formerly M0357 N0134)
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2
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1, 1, 2, 2, 6, 9, 17, 30, 54, 98, 183, 341, 645, 1220, 2327, 4451, 8555, 16489, 31859, 61717, 119779, 232919, 453584, 884544, 1727213, 3376505, 6607371, 12942012, 25371540, 49777187, 97731027, 192010355, 377475336, 742512992, 1461352025, 2877572478, 5668965407
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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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Table of n, a(n) for n=0..36.
Index entries for sequences related to populations of quadratic forms
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EXAMPLE
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a(4)=6 since 2^4=16 and 1=1^2, 4=2^2, 9=3^2, 12=12*1^2, 13=1^2+12*1^2, 16=4^2.
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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\12), issquare(k-12*y^2))))
(PARI) a(n)=local(A); if(n<0, 0, A=qfrep([1, 0; 0, 12], 2^n); sum(k=1, 2^n, A[k]!=0))
(Haskell)
a000021 n = length [() | k <- [1..2^n],
sum [a010052 (k - 12*y^2) | y <- [0..a000196 (k `div` 12)]] > 0]
-- Reinhard Zumkeller, Apr 16 2012
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CROSSREFS
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Cf. A000196, A010052.
Sequence in context: A094485 A188808 A021819 * A000022 A034805 A192659
Adjacent sequences: A000018 A000019 A000020 * A000022 A000023 A000024
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from David W. Wilson, Feb 07 2000.
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STATUS
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approved
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