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A205161 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..3 introduced in row major order.

%I A205161 #8 Jul 22 2025 18:35:33
%S A205161 1,2,2,4,15,4,12,159,159,12,40,2191,6941,2191,40,143,31168,332285,
%T A205161 332285,31168,143,528,447343,15821727,54314298,15821727,447343,528,
%U A205161 1979,6427791,754700909,8797534495,8797534495,754700909,6427791,1979,7466,92387812
%N A205161 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..3 introduced in row major order.
%C A205161 Table starts
%C A205161 ....1........2.............4................12....................40
%C A205161 ....2.......15...........159..............2191.................31168
%C A205161 ....4......159..........6941............332285..............15821727
%C A205161 ...12.....2191........332285..........54314298............8797534495
%C A205161 ...40....31168......15821727........8797534495.........4826926610498
%C A205161 ..143...447343.....754700909.....1427843505563......2654271236904226
%C A205161 ..528..6427791...35987024999...231638725420288...1458877292453477918
%C A205161 .1979.92387812.1716127952620.37582214286016391.801931987315155805350
%H A205161 R. H. Hardin, <a href="/A205161/b205161.txt">Table of n, a(n) for n = 1..84</a>
%e A205161 Some solutions for n=5 k=3
%e A205161 ..0..0..1....0..1..0....0..0..1....0..0..1....0..0..1....0..0..1....0..1..0
%e A205161 ..2..0..3....0..1..0....0..0..1....1..2..1....0..1..0....0..1..0....2..0..1
%e A205161 ..3..1..1....1..2..1....2..3..2....1..3..2....2..2..1....2..2..1....0..2..1
%e A205161 ..0..1..2....0..1..1....1..2..0....0..3..3....0..3..1....1..3..2....1..2..3
%e A205161 ..1..2..0....3..3..0....1..0..0....0..1..3....0..1..0....0..1..0....3..0..0
%Y A205161 Column 1 is A204678
%Y A205161 Column 2 is A204679
%K A205161 nonn,tabl
%O A205161 1,2
%A A205161 _R. H. Hardin_ Jan 22 2012