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Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).
1

%I #6 Jun 20 2022 19:14:35

%S 1212,6896,39188,222988,1269812,7237508,41285540,235717236,1346930052,

%T 7703391252,44093945060,252614282612,1448426221700,8312186475348,

%U 47741148641380,274441042958900,1578929657150788,9091864955315348

%N Number of (n+1) X (2+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234544/b234544.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) -30*a(n-2) -944*a(n-3) +5146*a(n-4) +8720*a(n-5) -112704*a(n-6) +148224*a(n-7) +392632*a(n-8) -632528*a(n-9) -548544*a(n-10) +867968*a(n-11) +341120*a(n-12) -478976*a(n-13) -76800*a(n-14) +92160*a(n-15).

%e Some solutions for n=3:

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

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

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

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

%Y Column 2 of A234549.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2013