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A234882 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 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 9

%I

%S 32,68,68,128,148,128,268,268,268,268,512,628,472,628,512,1068,1188,

%T 1116,1116,1188,1068,2048,2944,2096,3336,2096,2944,2048,4268,5684,

%U 5316,6364,6364,5316,5684,4268,8192,14604,10240,22748,12208,22748,10240,14604,8192

%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 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 32 68 128 268 512 1068 2048 4268 8192

%C 68 148 268 628 1188 2944 5684 14604 28492

%C 128 268 472 1116 2096 5316 10240 27060 52744

%C 268 628 1116 3336 6364 22748 44540 178572 353428

%C 512 1188 2096 6364 12208 44348 87312 354132 703104

%C 1068 2944 5316 22748 44348 261384 518988 3695496 7370908

%C 2048 5684 10240 44540 87312 518988 1035792 7389460 14782992

%C 4268 14604 27060 178572 354132 3695496 7389460 98517200 197023228

%C 8192 28492 52744 353428 703104 7370908 14782992 197023228 394703128

%C 17068 74816 142876 1512256 3038716 57766200 115949340 2946513328 5899223932

%H R. H. Hardin, <a href="/A234882/b234882.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-2) -4*a(n-4).

%F k=2: [order 9].

%F k=3: [order 11].

%F k=4: [order 19].

%F k=5: [order 23].

%F k=6: [order 31].

%F k=7: [order 35].

%e Some solutions for n=4, k=4:

%e 1 0 1 0 1 2 4 3 4 2 3 4 3 4 3 1 0 3 0 1

%e 4 2 4 2 4 0 3 1 3 0 1 3 1 3 1 4 2 4 2 4

%e 3 0 3 0 1 2 4 3 4 2 3 4 3 4 3 1 0 1 0 1

%e 4 2 4 2 4 1 2 0 2 1 0 2 0 2 0 4 2 4 2 4

%e 1 0 1 0 3 2 4 1 4 2 1 4 3 4 3 3 0 1 0 3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 01 2014

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Last modified September 30 07:52 EDT 2022. Contains 357104 sequences. (Running on oeis4.)