A221200 - OEIS

%I #4 Jan 04 2013 12:27:07

%S 0,1,0,2,9,0,4,10,49,0,8,196,46,289,0,16,720,9025,212,1681,0,32,6400,

%T 58700,427716,976,9801,0,64,34272,2518569,4984812,20277009,4492,57121,

%U 0,128,242064,32085376,1026177156,433687328,961434049,20672,332929,0,256

%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no occupancy greater than 2

%C Table starts

%C .0........1......2.............4.............8..............16.............32

%C .0........9.....10...........196...........720............6400..........34272

%C .0.......49.....46..........9025.........58700.........2518569.......32085376

%C .0......289....212........427716.......4984812......1026177156....30374196832

%C .0.....1681....976......20277009.....433687328....420771471561.29037336149952

%C .0.....9801...4492.....961434049...38397901048.172850051090025

%C .0....57121..20672...45583531009.3437301520640

%C .0...332929..95128.2161117565476

%C .0..1940449.437752

%C .0.11309769

%C .0

%C Even columns are perfect squares

%H R. H. Hardin, <a href="/A221200/b221200.txt">Table of n, a(n) for n = 1..71</a>

%e Some solutions for n=3 k=4

%e ..0..2..2..0....0..0..1..0....0..2..2..0....0..1..2..2....0..1..2..0

%e ..1..0..0..2....2..1..1..2....0..2..1..1....1..2..0..1....1..1..1..2

%e ..1..2..2..0....1..2..1..1....2..1..1..0....1..0..2..0....1..2..1..0

%Y Column 2 is A090390

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Jan 04 2013