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A205310 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

%I A205310 #8 Jul 22 2025 18:46:40
%S A205310 1,2,2,4,15,4,12,159,159,12,40,2191,7445,2191,40,143,31168,381958,
%T A205310 381958,31168,143,528,447343,19490790,70985206,19490790,447343,528,
%U A205310 1979,6427791,996536552,13049279920,13049279920,996536552,6427791,1979,7466,92387812
%N A205310 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.
%C A205310 Table starts
%C A205310 ....1........2.............4................12.....................40
%C A205310 ....2.......15...........159..............2191..................31168
%C A205310 ....4......159..........7445............381958...............19490790
%C A205310 ...12.....2191........381958..........70985206............13049279920
%C A205310 ...40....31168......19490790.......13049279920..........8615950028840
%C A205310 ..143...447343.....996536552.....2404472055439.......5705396521337690
%C A205310 ..528..6427791...50933680120...442834241887042....3775750320744043966
%C A205310 .1979.92387812.2603456557653.81565593153176155.2499057571450100571862
%H A205310 R. H. Hardin, <a href="/A205310/b205310.txt">Table of n, a(n) for n = 1..84</a>
%e A205310 Some solutions for n=5 k=3
%e A205310 ..0..0..1....0..0..1....0..0..1....0..1..0....0..0..1....0..0..1....0..1..1
%e A205310 ..0..1..0....1..2..1....0..2..0....0..2..1....0..1..1....2..0..2....0..2..1
%e A205310 ..2..2..1....1..3..2....3..1..1....1..0..0....2..0..2....2..1..1....1..1..0
%e A205310 ..1..3..2....0..3..3....2..0..2....3..1..3....2..1..0....0..1..1....3..2..3
%e A205310 ..0..1..0....0..1..3....0..1..0....0..1..0....3..2..2....2..2..3....3..0..0
%Y A205310 Column 1 is A204678
%Y A205310 Column 2 is A204679
%K A205310 nonn,tabl
%O A205310 1,2
%A A205310 _R. H. Hardin_ Jan 25 2012