A228848 a(n) = round(3*n^2/Pi^2).

0, 0, 1, 3, 5, 8, 11, 15, 19, 25, 30, 37, 44, 51, 60, 68, 78, 88, 98, 110, 122, 134, 147, 161, 175, 190, 205, 222, 238, 256, 274, 292, 311, 331, 351, 372, 394, 416, 439, 462, 486, 511, 536, 562, 588, 616, 643, 671, 700, 730, 760, 791, 822, 854, 886, 919, 953

Offset

0,4

Comments

a(n) is the asymptotic limit of A005728(n) and of A015614(n).

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 71 at p. 171.

Links

Table of n, a(n) for n=0..56.

Wikipedia, Farey sequence.

Formula

a(n) = round(A033428(n)/Pi^2).

a(n) ~ A104141*n^2.

Mathematica

Round[(3*Range[0, 60]^2)/Pi^2] (* Harvey P. Dale, Dec 18 2013 *)

Prog

(PARI) for(n=0, 56, print1(round(3*(n/Pi)^2), ", "))
(Sage) [round(3*n^2/pi^2) for n in range(0, 57)] # Stefano Spezia, Aug 06 2024

Crossrefs

Cf. A000796, A005728, A015614, A104141.

Sequence in context: A078126 A024206 A159325 * A049706 A080415 A340318

Adjacent sequences: A228845 A228846 A228847 * A228849 A228850 A228851

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Sep 05 2013

Status

approved