A000077 Number of positive integers <= 2^n of form x^2 + 6 y^2. (Formerly M1095 N0417)

1, 1, 2, 4, 8, 13, 24, 42, 76, 140, 257, 483, 907, 1717, 3272, 6261, 12027, 23172, 44769, 86708, 168245, 327073, 636849, 1241720, 2424290, 4738450, 9271396, 18157630, 35591729, 69820804, 137069245, 269270791, 529312776, 1041093937, 2048826229, 4034062310

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

Table of n, a(n) for n=0..35.

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

Example

a(3)=4 since 2^3=8 and 1=1^2, 4=2^2, 6=6*1^2, 7=1^2+6*1^2.

Prog

(PARI) a(n)=if(n<0, 0, sum(k=1, 2^n, 0<sum(y=0, sqrtint(k\6), issquare(k-6*y^2))))

Crossrefs

Sequence in context: A096573 A348574 A227910 * A054164 A226060 A262569

Adjacent sequences: A000074 A000075 A000076 * A000078 A000079 A000080

Keyword

nonn

Author

N. J. A. Sloane

Status

approved