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A196138 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 0,2,1,3,4 for x=0,1,2,3,4.

%I A196138 #7 Jun 02 2025 04:17:52
%S A196138 1,0,0,1,4,1,2,3,3,2,1,8,4,8,1,1,14,19,19,14,1,3,19,31,31,31,19,3,3,
%T A196138 46,70,165,165,70,46,3,2,56,117,251,326,251,117,56,2,4,133,253,931,
%U A196138 1350,1350,931,253,133,4,6,184,538,1880,3288,3716,3288,1880,538,184,6,5,372
%N A196138 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 0,2,1,3,4 for x=0,1,2,3,4.
%C A196138 Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
%C A196138 Table starts
%C A196138 .1...0....1.....2......1......1.......3........3.........2..........4
%C A196138 .0...4....3.....8.....14.....19......46.......56.......133........184
%C A196138 .1...3....4....19.....31.....70.....117......253.......538.......1169
%C A196138 .2...8...19....31....165....251.....931.....1880......5556......15236
%C A196138 .1..14...31...165....326...1350....3288....12943.....33772.....113604
%C A196138 .1..19...70...251...1350...3716...20706....63545....255501.....992477
%C A196138 .3..46..117...931...3288..20706...75720...384083...1662512....8212668
%C A196138 .3..56..253..1880..12943..63545..384083..2040678..11848389...73800939
%C A196138 .2.133..538..5556..33772.255501.1662512.11848389..86632050..560572499
%C A196138 .4.184.1169.15236.113604.992477.8212668.73800939.560572499.5257705657
%H A196138 R. H. Hardin, <a href="/A196138/b196138.txt">Table of n, a(n) for n = 1..219</a>
%e A196138 Some solutions for n=6 k=4
%e A196138 ..2..1..0..1....1..2..2..1....1..2..1..0....1..2..1..0....0..2..1..0
%e A196138 ..1..0..1..2....0..1..1..1....1..2..0..1....1..0..1..2....1..1..1..2
%e A196138 ..0..1..1..2....2..1..1..2....0..1..1..2....2..1..0..1....2..1..0..1
%e A196138 ..1..2..0..1....1..0..1..2....2..1..1..2....0..1..2..1....0..1..2..1
%e A196138 ..1..0..2..1....1..2..1..1....1..1..0..1....2..1..0..1....2..1..0..1
%e A196138 ..2..1..1..0....1..2..1..0....0..2..1..0....1..0..1..2....1..0..1..2
%Y A196138 Column 1 is A017817(n+3)
%K A196138 nonn,tabl
%O A196138 1,5
%A A196138 _R. H. Hardin_ Sep 28 2011