A210433 Natural numbers k such that floor(v) * ceiling(v)^2 = k, where v = k^(1/3).

0, 1, 4, 8, 18, 27, 48, 64, 100, 125, 180, 216, 294, 343, 448, 512, 648, 729, 900, 1000, 1210, 1331, 1584, 1728, 2028, 2197, 2548, 2744, 3150, 3375, 3840, 4096, 4624, 4913, 5508, 5832, 6498, 6859, 7600, 8000, 8820, 9261, 10164, 10648, 11638, 12167, 13248

Offset: 1

Author

John W. Layman, Mar 21 2012

Keywords

• nonn

Comments

a(n) is the number of undirected rook moves on a n X n chessboard, considered up to rotations and reflections. - Hilko Koning, Aug 09 2025

Crossrefs

Cf. A002620, A006501.

Programs

PARI

isok(k) = {cbr = sqrtnint(k, 3); if (cbr^3 == k, 1, cbr*(cbr+1)^2 == k);} \\ Michel Marcus, Jul 08 2014

Formula

It appears that a(n) = n^3/8 if n is even, a(n) = (n-1)*(n+1)^2/8 if n is odd.

Empirical g.f.: x^2*(x^3+x^2+3*x+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Jul 08 2014