This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A210433 #22 Aug 14 2025 19:43:26
%S A210433 0,1,4,8,18,27,48,64,100,125,180,216,294,343,448,512,648,729,900,1000,
%T A210433 1210,1331,1584,1728,2028,2197,2548,2744,3150,3375,3840,4096,4624,
%U A210433 4913,5508,5832,6498,6859,7600,8000,8820,9261,10164,10648,11638,12167,13248
%N A210433 Natural numbers k such that floor(v) * ceiling(v)^2 = k, where v = k^(1/3).
%C A210433 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
%F A210433 It appears that a(n) = n^3/8 if n is even, a(n) = (n-1)*(n+1)^2/8 if n is odd.
%F A210433 Empirical g.f.: x^2*(x^3+x^2+3*x+1) / ((x-1)^4*(x+1)^3). - _Colin Barker_, Jul 08 2014
%o A210433 (PARI) isok(k) = {cbr = sqrtnint(k, 3); if (cbr^3 == k, 1, cbr*(cbr+1)^2 == k);} \\ _Michel Marcus_, Jul 08 2014
%Y A210433 Cf. A002620, A006501.
%K A210433 nonn
%O A210433 1,3
%A A210433 _John W. Layman_, Mar 21 2012