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A204685 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.

%I A204685 #8 Jul 22 2025 18:14:14
%S A204685 1,2,2,4,15,4,12,159,159,12,40,2191,6451,2191,40,143,31168,287379,
%T A204685 287379,31168,143,528,447343,12711292,40919141,12711292,447343,528,
%U A204685 1979,6427791,563046972,5770321516,5770321516,563046972,6427791,1979,7466,92387812
%N A204685 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.
%C A204685 Table starts
%C A204685 ....1........2.............4..............12...............40..............143
%C A204685 ....2.......15...........159............2191............31168...........447343
%C A204685 ....4......159..........6451..........287379.........12711292........563046972
%C A204685 ...12.....2191........287379........40919141.......5770321516.....815364171994
%C A204685 ...40....31168......12711292......5770321516....2579588216958.1155411237719424
%C A204685 ..143...447343.....563046972....815364171994.1155411237719424
%C A204685 ..528..6427791...24932875448.115180678788869
%C A204685 .1979.92387812.1104148318540
%H A204685 R. H. Hardin, <a href="/A204685/b204685.txt">Table of n, a(n) for n = 1..60</a>
%e A204685 Some solutions for n=5 k=3
%e A204685 ..0..0..1....0..1..0....0..0..1....0..0..1....0..0..1....0..1..1....0..0..1
%e A204685 ..2..3..1....2..0..3....2..2..1....0..0..2....0..1..0....0..0..1....0..1..0
%e A204685 ..1..1..3....1..2..1....0..3..2....1..3..1....2..3..3....2..0..2....2..2..1
%e A204685 ..3..3..1....0..1..0....2..0..2....1..2..0....0..1..0....2..1..1....1..2..2
%e A204685 ..0..1..1....2..2..3....3..3..1....2..0..1....1..2..1....3..1..0....0..1..3
%K A204685 nonn,tabl
%O A204685 1,2
%A A204685 _R. H. Hardin_ Jan 18 2012