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%I #7 Sep 09 2022 12:05:53
%S 4,22,95,546,2765,14503,74812,386556,2008698,10415923,54096117,
%T 280793815,1457402796,7564115674,39256668738,203743660496,
%U 1057439556784,5488205547156,28484308704921,147836021658293,767281388051654
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.
%C 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 Column 3 of A197672.
%H R. H. Hardin, <a href="/A197667/b197667.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 5*a(n-1) +7*a(n-2) -24*a(n-3) -44*a(n-4) +67*a(n-5) +50*a(n-6) -412*a(n-7) -2205*a(n-8) -7418*a(n-9) -6654*a(n-10) -2331*a(n-11) +42455*a(n-12) +97689*a(n-13) +188061*a(n-14) +169272*a(n-15) -162775*a(n-16) -268709*a(n-17) -801522*a(n-18) -429147*a(n-19) +162997*a(n-20) -228546*a(n-21) +1079921*a(n-22) +1138660*a(n-23) +160033*a(n-24) -1361447*a(n-25) -51481*a(n-26) +285711*a(n-27) +152964*a(n-28) -624541*a(n-29) +374389*a(n-30) +62069*a(n-31) -30580*a(n-32) +83333*a(n-33) -134862*a(n-34) +17843*a(n-35) +16897*a(n-36) +7673*a(n-37) -3585*a(n-38) -1901*a(n-39) +2034*a(n-40) -729*a(n-41) +137*a(n-42) -105*a(n-43).
%e Some solutions for n=4
%e ..0..0..0....0..0..1....1..0..0....0..1..2....1..1..0....0..3..0....0..0..0
%e ..0..3..1....0..0..2....1..0..3....0..1..1....0..1..2....0..0..0....1..2..0
%e ..0..0..1....1..1..1....1..2..0....1..1..0....0..1..1....0..2..1....2..1..0
%e ..1..1..2....2..1..0....0..1..1....2..1..0....1..2..0....0..1..2....0..1..1
%Y Cf. A197672.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 17 2011
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