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%I #6 Jun 20 2022 20:59:54
%S 70,220,220,618,546,618,1954,1240,1240,1954,5506,3384,2390,3384,5506,
%T 17518,8416,5710,5710,8416,17518,49506,24420,12750,11982,12750,24420,
%U 49506,158518,64240,33946,23830,23830,33946,64240,158518,449170,194124
%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 4 (constant-stress 1 X 1 tilings).
%C Table starts
%C 70 220 618 1954 5506 17518 49506 158518 449170
%C 220 546 1240 3384 8416 24420 64240 194124 527920
%C 618 1240 2390 5710 12750 33946 83438 238306 621918
%C 1954 3384 5710 11982 23830 57210 128614 339234 831334
%C 5506 8416 12750 23830 42982 94114 195558 479914 1108726
%C 17518 24420 33946 57210 94114 187686 358450 810702 1742578
%C 49506 64240 83438 128614 195558 358450 635654 1336954 2694006
%C 158518 194124 238306 339234 479914 810702 1336954 2614518 4927738
%C 449170 527920 621918 831334 1108726 1742578 2694006 4927738 8740870
%C 1447510 1640076 1862530 2348514 2964106 4339470 6297370 10773174 17998810
%H R. H. Hardin, <a href="/A234564/b234564.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k: (column 2..7 recurrence works also for k=1; apparently all rows and columns satisfy the same order 14 recurrence):
%F k=1: a(n) = 3*a(n-1) +18*a(n-2) -54*a(n-3) -80*a(n-4) +240*a(n-5).
%F k=2..7: [same order 14 recurrence].
%e Some solutions for n=5, k=4:
%e 4 0 4 0 4 4 1 4 1 2 0 3 1 2 0 3 2 4 2 3
%e 2 2 2 2 2 2 3 2 3 0 2 1 3 0 2 1 4 2 4 1
%e 4 0 4 0 4 4 1 4 1 2 0 3 1 2 0 3 2 4 2 3
%e 2 2 2 2 2 3 4 3 4 1 2 1 3 0 2 1 4 2 4 1
%e 0 4 0 4 0 4 1 4 1 2 0 3 1 2 0 1 0 2 0 1
%e 0 0 0 0 0 3 4 3 4 1 2 1 3 0 2 1 4 2 4 1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 28 2013