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A000077 Number of positive integers <= 2^n of form x^2 + 6 y^2.
(Formerly M1095 N0417)
0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

LINKS

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

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: A227232 A096573 A227910 * A054164 A226060 A262569

Adjacent sequences:  A000074 A000075 A000076 * A000078 A000079 A000080

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 26 12:21 EDT 2017. Contains 287095 sequences.