Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jun 19 2022 02:21:21
%S 136,512,512,1880,1544,1880,7072,4724,4724,7072,26040,15604,12176,
%T 15604,26040,98080,51144,35868,35868,51144,98080,361688,176104,105208,
%U 96848,105208,176104,361688,1364512,597712,333340,261760,261760,333340,597712
%N T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
%C Table starts
%C 136 512 1880 7072 26040 98080 361688 1364512
%C 512 1544 4724 15604 51144 176104 597712 2109748
%C 1880 4724 12176 35868 105208 333340 1043256 3446068
%C 7072 15604 35868 96848 261760 774140 2263256 7020392
%C 26040 51144 105208 261760 652872 1816160 4984584 14642048
%C 98080 176104 333340 774140 1816160 4812096 12604104 35505020
%C 361688 597712 1043256 2263256 4984584 12604104 31498952 85424552
%C 1364512 2109748 3446068 7020392 14642048 35505020 85424552 224694240
%C 5038200 7324940 11230320 21497244 42396520 98577596 227963432 582078148
%C 19038496 26321996 38241780 68985912 129109408 287939516 642257224 1596252448
%H R. H. Hardin, <a href="/A235198/b235198.txt">Table of n, a(n) for n = 1..197</a>
%F Empirical for column k (the k=3..6 recurrence works also for k=1..2; apparently all rows and columns satisfy the same order 39 recurrence):
%F k=1: a(n) = 30*a(n-2) -257*a(n-4) +468*a(n-6).
%F k=2: [order 23].
%F k=3..6: [same order 39 recurrence].
%e Some solutions for n=4, k=4:
%e 1 4 2 5 1 2 6 3 4 3 3 6 4 6 3 1 4 1 5 2
%e 2 0 3 1 2 3 2 4 0 4 5 3 6 3 5 5 3 5 4 6
%e 1 4 2 5 1 1 5 2 3 2 1 4 2 4 1 2 5 2 6 3
%e 3 1 4 2 3 4 3 5 1 5 3 1 4 1 3 3 1 3 2 4
%e 0 3 1 4 0 1 5 2 3 2 1 4 2 4 1 0 3 0 4 1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 04 2014