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%I #7 Jun 18 2022 23:38:15
%S 20,40,40,68,68,68,136,104,104,136,236,188,148,188,236,472,304,248,
%T 248,304,472,836,572,380,380,380,572,836,1672,968,680,544,544,680,968,
%U 1672,3020,1868,1108,908,740,908,1108,1868,3020,6040,3280,2072,1400,1168,1168
%N T(n,k) is the number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).
%C Table starts
%C 20 40 68 136 236 472 836 1672 3020 6040 11108 22216 41516
%C 40 68 104 188 304 572 968 1868 3280 6428 11624 22988 42544
%C 68 104 148 248 380 680 1108 2072 3548 6824 12148 23768 43580
%C 136 188 248 380 544 908 1400 2492 4096 7628 13208 25340 45664
%C 236 304 380 544 740 1168 1724 2944 4676 8464 14300 26944 47780
%C 472 572 680 908 1168 1724 2408 3884 5872 10172 16520 30188 52048
%C 836 968 1108 1400 1724 2408 3220 4952 7196 12008 18868 33560 56444
%C 1672 1868 2072 2492 2944 3884 4952 7196 9952 15788 23672 40412 65344
%C 3020 3280 3548 4096 4676 5872 7196 9952 13220 20080 28988 47776 74756
%C 6040 6428 6824 7628 8464 10172 12008 15788 20080 28988 39944 62828 93904
%C Empirical: T(n,k) is the number of (n+1) X (k+1) 0..2+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2+2*i (constant-stress 1 X 1 tilings) for i=1..4(..?).
%H R. H. Hardin, <a href="/A235289/b235289.txt">Table of n, a(n) for n = 1..568</a>
%F Empirical for column k (the recurrence for k=2..7 also works for k=1; apparently every row and column satisfies the same order 6 recurrence):
%F diagonal: a(n) = a(n-1) +9*a(n-2) -9*a(n-3) -26*a(n-4) +26*a(n-5) +24*a(n-6) -24*a(n-7).
%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -6*a(n-3).
%F k=2..7: a(n) = 3*a(n-1) +3*a(n-2) -15*a(n-3) +4*a(n-4) +18*a(n-5) -12*a(n-6).
%e Some solutions for n=4, k=4:
%e 2 0 2 0 2 2 0 2 0 1 2 1 2 0 2 1 3 1 3 2
%e 1 3 1 3 1 1 3 1 3 0 0 3 0 2 0 2 0 2 0 3
%e 3 1 3 1 3 2 0 2 0 1 3 2 3 1 3 0 2 0 2 1
%e 0 2 0 2 0 1 3 1 3 0 0 3 0 2 0 2 0 2 0 3
%e 2 0 2 0 2 2 0 2 0 1 3 2 3 1 3 0 2 0 2 1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 05 2014
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