|
| |
|
|
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; 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
| 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: A074467 A018066 A096573 * A054164 A102704 A196720
Adjacent sequences: A000074 A000075 A000076 * A000078 A000079 A000080
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
