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A196957 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 2,1,3,4,0 for x=0,1,2,3,4.

%I A196957 #7 Jun 02 2025 04:39:00
%S A196957 1,2,2,3,5,3,4,9,9,4,6,20,26,20,6,9,41,87,87,41,9,13,85,282,492,282,
%T A196957 85,13,19,178,919,2687,2687,919,178,19,28,369,2987,14509,23956,14509,
%U A196957 2987,369,28,41,769,9722,78717,214124,214124,78717,9722,769,41,60,1600,31643
%N A196957 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 2,1,3,4,0 for x=0,1,2,3,4.
%C A196957 Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 4's, every 4 is next to 4 0's
%C A196957 Table starts
%C A196957 ..1....2......3........4..........6............9.............13
%C A196957 ..2....5......9.......20.........41...........85............178
%C A196957 ..3....9.....26.......87........282..........919...........2987
%C A196957 ..4...20.....87......492.......2687........14509..........78717
%C A196957 ..6...41....282.....2687......23956.......214124........1918608
%C A196957 ..9...85....919....14509.....214124......3166711.......46887039
%C A196957 .13..178...2987....78717....1918608.....46887039.....1147966466
%C A196957 .19..369...9722...427700...17197531....695103098....28133304588
%C A196957 .28..769..31643..2320738..154075730..10297360567...688970472958
%C A196957 .41.1600.102962.12593583.1380294235.152533682507.16871844816740
%H A196957 R. H. Hardin, <a href="/A196957/b196957.txt">Table of n, a(n) for n = 1..364</a>
%e A196957 Some solutions for n=6 k=4
%e A196957 ..0..0..0..0....0..1..0..0....1..1..0..0....0..1..0..0....0..0..0..0
%e A196957 ..1..0..1..1....0..1..0..0....0..0..1..1....0..1..0..0....0..0..1..0
%e A196957 ..1..0..0..0....0..0..0..0....1..1..0..0....1..0..0..0....0..0..1..0
%e A196957 ..0..0..1..1....0..0..0..0....0..0..4..0....1..0..4..0....0..0..0..1
%e A196957 ..1..0..0..0....0..1..0..0....0..0..0..0....0..4..0..0....1..1..0..1
%e A196957 ..1..0..0..0....0..1..0..0....0..1..1..0....0..0..1..1....0..0..0..0
%Y A196957 Column 1 is A000930(n+1)
%Y A196957 Column 2 is A105309(n+1)
%K A196957 nonn,tabl
%O A196957 1,2
%A A196957 _R. H. Hardin_ Oct 08 2011