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%I #8 Jun 20 2022 21:04:20
%S 32,120,120,448,582,448,1680,2804,2804,1680,6272,13676,17200,13676,
%T 6272,23520,66228,108404,108404,66228,23520,87808,324556,666880,
%U 896112,666880,324556,87808,329280,1578036,4221580,7165920,7165920,4221580,1578036
%N T(n,k) is the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).
%C Table starts
%C 32 120 448 1680 6272 23520
%C 120 582 2804 13676 66228 324556
%C 448 2804 17200 108404 666880 4221580
%C 1680 13676 108404 896112 7165920 59991972
%C 6272 66228 666880 7165920 72539432 790261148
%C 23520 324556 4221580 59991972 790261148 11533082488
%C 87808 1578036 26023136 483370700 8028682984 153582428536
%C 329280 7767916 165444308 4098064360 88710949848 2303823299344
%C 1229312 37908724 1021780992 33256428216 904037477472 30988558369076
%C 4609920 187373548 6523295060 285401797556 10133236760728 477592381790200
%H R. H. Hardin, <a href="/A234443/b234443.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 14*a(n-2).
%F k=2: a(n) = 5*a(n-1) +24*a(n-2) -130*a(n-3) +36*a(n-4) +80*a(n-5) -32*a(n-6).
%F k=3: [order 16].
%F k=4: [order 45].
%e Some solutions for n=3, k=4:
%e 1 1 1 2 1 0 1 0 0 0 1 0 1 0 2 0 1 1 1 0
%e 2 1 0 2 0 2 2 2 1 0 0 0 0 0 1 1 1 2 1 1
%e 2 0 0 1 0 1 0 1 1 1 1 2 1 0 2 1 2 2 0 1
%e 2 1 0 2 0 2 2 2 1 2 0 2 0 0 1 2 2 1 0 0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 26 2013
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