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A197672 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 4,0,1,0,1 for x=0,1,2,3,4.

%I A197672 #7 Jun 02 2025 05:04:50
%S A197672 1,3,3,4,9,4,5,22,22,5,9,71,95,71,9,16,217,546,546,217,16,25,642,2765,
%T A197672 5005,2765,642,25,39,1963,14503,44323,44323,14503,1963,39,64,5963,
%U A197672 74812,403960,709083,403960,74812,5963,64,105,18018,386556,3675345,11277331
%N A197672 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 4,0,1,0,1 for x=0,1,2,3,4.
%C A197672 Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's
%C A197672 Table starts
%C A197672 ...1.....3........4..........5............9..............16................25
%C A197672 ...3.....9.......22.........71..........217.............642..............1963
%C A197672 ...4....22.......95........546.........2765...........14503.............74812
%C A197672 ...5....71......546.......5005........44323..........403960...........3675345
%C A197672 ...9...217.....2765......44323.......709083........11277331.........178113620
%C A197672 ..16...642....14503.....403960.....11277331.......311676959........8613257822
%C A197672 ..25..1963....74812....3675345....178113620......8613257822......417293944115
%C A197672 ..39..5963...386556...33272751...2824369075....239118653300....20252638815131
%C A197672 ..64.18018..2008698..301565202..44803424135...6630227642552...981414876628367
%C A197672 .105.54753.10415923.2734015025.710299706355.183756345226485.47569549221404522
%H A197672 R. H. Hardin, <a href="/A197672/b197672.txt">Table of n, a(n) for n = 1..143</a>
%e A197672 Some solutions containing all values 0 to 4 for n=6 k=4
%e A197672 ..0..3..0..0....1..1..2..1....0..1..2..0....1..0..0..0....0..2..1..0
%e A197672 ..0..0..0..3....0..0..0..0....1..4..1..0....2..0..3..0....0..1..4..1
%e A197672 ..0..0..3..0....0..3..0..0....2..1..1..0....1..0..1..2....0..1..1..1
%e A197672 ..2..1..2..0....0..2..1..2....0..0..3..0....1..1..4..1....0..3..0..0
%e A197672 ..1..4..1..0....0..1..4..1....0..3..0..0....0..1..1..0....0..0..0..0
%e A197672 ..0..1..1..0....0..2..1..0....1..1..0..0....0..1..1..0....0..0..3..0
%Y A197672 Column 1 is A195971
%K A197672 nonn,tabl
%O A197672 1,2
%A A197672 _R. H. Hardin_ Oct 17 2011