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A196456 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,4,1 for x=0,1,2,3,4.

%I A196456 #7 Jun 02 2025 04:24:41
%S A196456 1,3,3,4,6,4,5,14,14,5,8,30,40,30,8,12,67,131,131,67,12,17,146,383,
%T A196456 594,383,146,17,25,320,1232,2930,2930,1232,320,25,37,706,3966,15274,
%U A196456 27320,15274,3966,706,37,54,1550,12314,76809,249402,249402,76809,12314,1550,54
%N A196456 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,4,1 for x=0,1,2,3,4.
%C A196456 Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 2's, every 3 is next to 3 4's, every 4 is next to 4 1's
%C A196456 Table starts
%C A196456 ..1....3......4.......5..........8..........12............17..............25
%C A196456 ..3....6.....14......30.........67.........146...........320.............706
%C A196456 ..4...14.....40.....131........383........1232..........3966...........12314
%C A196456 ..5...30....131.....594.......2930.......15274.........76809..........380093
%C A196456 ..8...67....383....2930......27320......249402.......2032584........15952022
%C A196456 .12..146...1232...15274.....249402.....3707781......46887621.......578160718
%C A196456 .17..320...3966...76809....2032584....46887621.....926499600.....17962317556
%C A196456 .25..706..12314..380093...15952022...578160718...17962317556....539621963877
%C A196456 .37.1550..38745.1900745..128543371..7394096617..351103877665..16067939829696
%C A196456 .54.3403.122989.9527317.1060801262.96338727461.6945098996988.486076221745274
%H A196456 R. H. Hardin, <a href="/A196456/b196456.txt">Table of n, a(n) for n = 1..161</a>
%e A196456 Some solutions for n=6 k=4
%e A196456 ..0..0..1..1....0..1..1..0....1..0..0..0....0..0..0..1....0..0..0..1
%e A196456 ..1..1..1..0....2..2..1..0....1..0..0..0....1..1..1..1....0..0..2..2
%e A196456 ..1..1..4..1....2..2..1..0....2..2..0..0....2..2..2..0....0..0..2..2
%e A196456 ..0..0..1..1....0..1..1..0....2..2..0..0....2..0..2..0....2..2..1..0
%e A196456 ..0..2..2..0....0..1..1..1....0..0..0..0....2..2..2..0....2..2..1..1
%e A196456 ..1..2..2..1....1..1..0..1....1..1..1..1....0..0..0..0....0..0..0..1
%Y A196456 Column 1 is A179070(n+2)
%K A196456 nonn,tabl
%O A196456 1,2
%A A196456 _R. H. Hardin_ Oct 02 2011