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A194505 T(n,k)=Number of lower triangles of an n X n 0..k array with each element unequal to the sum mod k+1 of its horizontal and vertical neighbors.

%I A194505 #8 Jul 22 2025 12:34:25
%S A194505 1,2,1,3,8,4,4,27,72,2,5,64,776,1020,1,6,125,4160,59052,32768,1,7,216,
%T A194505 15804,1048560,14348907,2097152,1,8,343,46872,9765630,1073741824,
%U A194505 10460353203,268460064,16,9,512,118096,60466140,30517578125
%N A194505 T(n,k)=Number of lower triangles of an n X n 0..k array with each element unequal to the sum mod k+1 of its horizontal and vertical neighbors.
%C A194505 Table starts
%C A194505 .1.........2..............3.................4....................5
%C A194505 .1.........8.............27................64..................125
%C A194505 .4........72............776..............4160................15804
%C A194505 .2......1020..........59052...........1048560..............9765630
%C A194505 .1.....32768.......14348907........1073741824..........30517578125
%C A194505 .1...2097152....10460353203.....4398046511104......476837158203125
%C A194505 .1.268460064.22876792454961.72057594037927936.37252902986083985625
%H A194505 R. H. Hardin, <a href="/A194505/b194505.txt">Table of n, a(n) for n = 1..62</a>
%e A194505 Some solutions for n=4 k=3
%e A194505 ..3........0........1........1........1........2........2........0
%e A194505 ..2.1......1.1......3.2......3.3......3.2......3.0......3.0......1.2
%e A194505 ..1.2.1....2.3.2....1.1.2....2.3.1....2.1.1....2.3.1....3.0.1....0.3.1
%e A194505 ..2.0.1.3..0.0.0.3..0.1.3.1..1.2.1.0..0.3.3.0..3.3.0.1..1.3.0.3..2.3.3.1
%Y A194505 Column 1 is A144260(n+1)
%K A194505 nonn,tabl
%O A194505 1,2
%A A194505 _R. H. Hardin_ Aug 27 2011