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A000021 Number of positive integers <= 2^n of form x^2 + 12 y^2.
(Formerly M0357 N0134)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
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).
LINKS
Delbert L. Johnson, Table of n, a(n) for n = 0..45
D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A021819 A359896 A339426 * A367718 A000022 A034805
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Feb 07 2000
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)