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A235319 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 7 (constant-stress 1 X 1 tilings). 9

%I #9 Jun 18 2022 23:01:13

%S 112,392,392,1120,1120,1120,3920,2744,2744,3920,11776,8392,5968,8392,

%T 11776,41216,22568,16352,16352,22568,41216,128128,71896,40144,40144,

%U 40144,71896,128128,448448,206360,118160,89600,89600,118160,206360

%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 7 (constant-stress 1 X 1 tilings).

%C Table starts

%C 112 392 1120 3920 11776 41216 128128 448448

%C 392 1120 2744 8392 22568 71896 206360 675064

%C 1120 2744 5968 16352 40144 118160 316912 978320

%C 3920 8392 16352 40144 89600 241600 598976 1723456

%C 11776 22568 40144 89600 184144 459536 1062832 2873552

%C 41216 71896 118160 241600 459536 1062832 2291696 5805424

%C 128128 206360 316912 598976 1062832 2291696 4632208 11046512

%C 448448 675064 978320 1723456 2873552 5805424 11046512 24862768

%C 1426432 2026472 2793040 4616960 7275856 13828496 24862768 52954448

%C 4992512 6751000 8912144 13917952 20859728 37480816 63985520 129456304

%C Empirical: T(n,k) is the number of (n+1) X (k+1) 0..5+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).

%H R. H. Hardin, <a href="/A235319/b235319.txt">Table of n, a(n) for n = 1..260</a>

%F Empirical for column k (the k=2..6 recurrence also works for k=1; apparently all rows and columns satisfy the same order 18 recurrence):

%F k=1: a(n) = 28*a(n-2) - 252*a(n-4) + 720*a(n-6).

%F k=2..6: [same order 18 recurrence]

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

%e 5 4 6 1 5 2 4 2 4 2 1 6 2 4 2 3 0 3 0 3

%e 0 6 1 3 0 6 1 6 1 6 4 2 5 0 5 1 5 1 5 1

%e 4 3 5 0 4 3 5 3 5 3 0 5 1 3 1 5 2 5 2 5

%e 0 6 1 3 0 5 0 5 0 5 4 2 5 0 5 2 6 2 6 2

%e 4 3 5 0 4 2 4 2 4 2 1 6 2 4 2 3 0 3 0 3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 05 2014

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)