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

Author

Arkadiusz Wesolowski, Sep 05 2013

Keywords

• nonn
• easy

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

• Wikipedia, Farey sequence.

Crossrefs

Cf. A000796, A005728, A015614, A104141.

Programs

Mathematica

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

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

Formula

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

a(n) ~ A104141*n^2.