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%I #17 Sep 04 2023 21:48:08
%S 1,1,1,1,2,1,1,5,5,1,1,8,15,8,1,1,18,46,46,18,1,1,37,156,231,156,37,1,
%T 1,73,507,1221,1221,507,73,1,1,151,1637,6284,10649,6284,1637,151,1,1,
%U 306,5338,32754,89527,89527,32754,5338,306,1,1,621,17401,170928,750414,1209990,750414,170928,17401,621,1
%N T(n,k) = number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,2,1,2 for x=0,1,2,3,4.
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 2's.
%H R. H. Hardin, <a href="/A197242/b197242.txt">Table of n, a(n) for n = 1..180</a>
%e Table starts:
%e 1 1 1 1 1 1 1 1
%e 1 2 5 8 18 37 73 151
%e 1 5 15 46 156 507 1637 5338
%e 1 8 46 231 1221 6284 32754 170928
%e 1 18 156 1221 10649 89527 750414 6315333
%e 1 37 507 6284 89527 1209990 16248436 220537819
%e 1 73 1637 32754 750414 16248436 352842084 7724652441
%e 1 151 5338 170928 6315333 220537819 7724652441 271939715540
%e 1 306 17401 888997 53202193 2991520965 168523962450 9558380534198
%e 1 621 56648 4628482 448046100 40512793371 3676078979774 336139854722483
%e ...
%e Some solutions containing all values 0 to 4 for n=6 and k=4:
%e 2 2 1 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 2 2
%e 2 2 3 1 0 2 4 2 2 2 2 0 0 2 2 2 0 2 4 2
%e 0 0 1 0 1 2 2 2 2 4 2 0 0 2 4 2 0 2 2 2
%e 2 2 2 0 3 1 0 1 2 2 2 1 0 2 2 2 0 1 0 0
%e 2 4 2 0 1 1 1 3 0 0 1 3 0 1 0 0 0 3 1 0
%e 2 2 2 0 1 3 1 1 0 0 0 1 1 3 1 0 0 1 0 0
%Y Columns 2..7 are A197211, A197237, A197238, A197239, A197240, A197241.
%Y Main diagonal is A197236.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Oct 12 2011
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