A000021 Number of positive integers <= 2^n of form x^2 + 12 y^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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			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.
		

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.
• Index entries for sequences related to populations of quadratic forms

Crossrefs

Cf. A000196, A010052, A272933.

Programs

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

PARI

a(n)=if(n<0,0,sum(k=1,2^n,0
				

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))

Extensions

More terms from David W. Wilson, Feb 07 2000