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%I #6 Jun 20 2022 18:13:29
%S 856,3164,10640,43680,163352,706992,2734000,12203144,47902816,
%T 218388912,864693472,4003619480,15940068144,74661520248,298373769264,
%U 1409767189888,5648661963120,26865714384208,107846686617472,515515002119648
%N Number of (n+1) X (3+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
%H R. H. Hardin, <a href="/A234885/b234885.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +86*a(n-2) -171*a(n-3) -3254*a(n-4) +6420*a(n-5) +72208*a(n-6) -140996*a(n-7) -1058026*a(n-8) +2037844*a(n-9) +10934873*a(n-10) -20686144*a(n-11) -83167418*a(n-12) +153691479*a(n-13) +479339096*a(n-14) -859425200*a(n-15) -2137842471*a(n-16) +3687468872*a(n-17) +7489913552*a(n-18) -12299566373*a(n-19) -20830586705*a(n-20) +32156843576*a(n-21) +46298748518*a(n-22) -66176437253*a(n-23) -82513440614*a(n-24) +107256565124*a(n-25) +117915942463*a(n-26) -136506202014*a(n-27) -134651989808*a(n-28) +135526272729*a(n-29) +121980787038*a(n-30) -103852594014*a(n-31) -86649823814*a(n-32) +60484275256*a(n-33) +47465104086*a(n-34) -26205941074*a(n-35) -19592874823*a(n-36) +8200629244*a(n-37) +5905922924*a(n-38) -1777329681*a(n-39) -1244167978*a(n-40) +250186878*a(n-41) +171453636*a(n-42) -20378088*a(n-43) -13746096*a(n-44) +723168*a(n-45) +482112*a(n-46).
%e Some solutions for n=4:
%e 2 3 2 3 3 2 5 4 5 2 5 4 3 1 3 1 5 3 5 4
%e 3 5 3 5 2 0 2 0 2 0 2 0 4 3 4 3 4 1 2 0
%e 1 4 1 4 5 4 5 4 4 1 4 3 2 0 2 0 5 3 5 2
%e 0 2 0 2 2 0 2 0 2 0 2 0 5 2 5 2 4 1 2 0
%e 1 4 1 4 4 1 4 1 5 4 5 4 2 0 4 0 5 3 5 4
%Y Column 3 of A234890.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 01 2014
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