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%I #6 Jun 20 2022 20:58:39
%S 104,436,436,1824,1560,1824,7696,5612,5612,7696,32384,20724,17448,
%T 20724,32384,137536,76972,56936,56936,76972,137536,582144,293316,
%U 188040,167688,188040,293316,582144,2488576,1123724,648536,503272,503272,648536
%N T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).
%C Table starts
%C 104 436 1824 7696 32384 137536 582144
%C 436 1560 5612 20724 76972 293316 1123724
%C 1824 5612 17448 56936 188040 648536 2264904
%C 7696 20724 56936 167688 503272 1597896 5162984
%C 32384 76972 188040 503272 1379816 4055128 12178344
%C 137536 293316 648536 1597896 4055128 11145960 31418264
%C 582144 1123724 2264904 5162984 12178344 31418264 83324136
%C 2488576 4410276 8215256 17479656 38671960 94267656 236748824
%C 10594304 17381356 30142344 60126376 125308904 289507096 690049704
%C 45577216 70026180 114224792 215032104 425135512 935746056 2128516184
%H R. H. Hardin, <a href="/A234227/b234227.txt">Table of n, a(n) for n = 1..179</a>
%F Empirical for column k (the k=4 recurrence also works for k=1..3; apparently the same order 16 recurrence works for all rows and columns):
%F k=1: a(n) = 4*a(n-1) +20*a(n-2) -80*a(n-3).
%F k=2: a(n) = 7*a(n-1) +20*a(n-2) -224*a(n-3) +144*a(n-4) +1680*a(n-5) -2880*a(n-6).
%F k=3: [order 11].
%F k=4: [order 16].
%F k=5: [same order 16].
%F k=6: [same order 16].
%F k=7: [same order 16].
%e Some solutions for n=4, k=4:
%e 0 0 2 0 2 4 1 3 1 3 1 1 2 0 1 3 1 0 1 0
%e 0 3 2 3 2 4 4 3 4 3 1 4 2 3 1 1 2 4 2 4
%e 0 0 2 0 2 1 4 0 4 0 2 2 3 1 2 3 1 0 1 0
%e 1 4 3 4 3 4 4 3 4 3 0 3 1 2 0 3 4 0 4 0
%e 4 4 0 4 0 4 1 3 1 3 2 2 3 1 2 0 4 3 4 3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 21 2013
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