|
%I #6 Jun 20 2022 20:29:36
%S 240,1096,1096,4192,3976,4192,19120,12464,12464,19120,74496,48976,
%T 33560,48976,74496,339328,168928,116168,116168,168928,339328,1344640,
%U 692512,360760,357208,360760,692512,1344640,6116416,2531888,1349336,1000264
%N T(n,k) is the number of (n+1) X (k+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7 (constant-stress 1 X 1 tilings).
%C Table starts
%C 240 1096 4192 19120 74496 339328 1344640
%C 1096 3976 12464 48976 168928 692512 2531888
%C 4192 12464 33560 116168 360760 1349336 4577624
%C 19120 48976 116168 357208 1000264 3403528 10632200
%C 74496 168928 360760 1000264 2557656 8002936 23194936
%C 339328 692512 1349336 3403528 8002936 23137720 62379416
%C 1344640 2531888 4577624 10632200 23194936 62379416 157274648
%C 6116416 10649920 17961560 38594056 78550072 197412088 467509400
%C 24606720 40456096 64580152 129877960 248588376 587074168 1311421240
%C 111778816 173104096 261840344 493469896 891039928 1982807032 4191830168
%H R. H. Hardin, <a href="/A234728/b234728.txt">Table of n, a(n) for n = 1..159</a>
%F Empirical for column k (k=2 recurrence also works for k=1; apparently all rows and columns satisfy the same order 30 recurrence):
%F k=1: a(n) = 68*a(n-2) -1724*a(n-4) +19312*a(n-6) -80640*a(n-8).
%F k=2..5: [same order 30 recurrence].
%e Some solutions for n=3, k=4:
%e 0 3 1 3 0 2 7 2 7 2 6 0 5 0 4 0 5 1 6 1
%e 5 1 6 1 5 3 1 3 1 3 4 5 3 5 2 6 4 7 5 7
%e 4 7 5 7 4 1 6 1 6 1 6 0 5 0 4 0 5 1 6 1
%e 5 1 6 1 5 5 3 5 3 5 3 4 2 4 1 4 2 5 3 5
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 30 2013
| 