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 A234564 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). 9

%I

%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

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Last modified December 4 21:40 EST 2022. Contains 358570 sequences. (Running on oeis4.)