%I #8 Feb 22 2020 20:54:24

%S 1,2,2,3,8,3,5,18,18,5,8,50,33,50,8,13,128,86,86,128,13,21,338,231,

%T 265,231,338,21,34,882,639,883,883,639,882,34,55,2312,1724,2974,3716,

%U 2974,1724,2312,55,89,6050,4697,9940,15780,15780,9940,4697,6050,89,144,15842

%N T(n,k) = Number of n X k 0..1 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order.

%C Table starts

%C ..1....2....3.....5......8......13.......21........34.........55..........89

%C ..2....8...18....50....128.....338......882......2312.......6050.......15842

%C ..3...18...33....86....231.....639.....1724......4697......12763.......34668

%C ..5...50...86...265....883....2974.....9940.....33462.....112470......377908

%C ..8..128..231...883...3716...15780....67169....286470....1221769.....5217560

%C .13..338..639..2974..15780...85681...461894...2501104...13632039....74052393

%C .21..882.1724..9940..67169..461894..3162172..21906411..152100304..1053377463

%C .34.2312.4697.33462.286470.2501104.21906411.193490711.1711765962.15187321948

%H R. H. Hardin, <a href="/A204197/b204197.txt">Table of n, a(n) for n = 1..576</a>

%e Some solutions for n=5 k=3

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

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

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

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

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

%Y Column 1 is A000045(n+1).

%Y Column 2 is A175395(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 12 2012