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Number of (n+1) X (4+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings).
1

%I #6 Jun 20 2022 19:52:25

%S 27344,69336,174320,531984,1602224,5614248,19258400,74809368,

%T 282312464,1187833176,4822708640,21611172984,92875010384,437216431128,

%U 1962918959840,9597345360888,44533050266384,224048187428376

%N Number of (n+1) X (4+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234686/b234686.txt">Table of n, a(n) for n = 1..116</a>

%F Empirical: a(n) = 8*a(n-1) +136*a(n-2) -1228*a(n-3) -7714*a(n-4) +83412*a(n-5) +227220*a(n-6) -3310020*a(n-7) -3144813*a(n-8) +85322244*a(n-9) -10139052*a(n-10) -1502272464*a(n-11) +1272592288*a(n-12) +18484107136*a(n-13) -25856757520*a(n-14) -159615082880*a(n-15) +298588477264*a(n-16) +954259846848*a(n-17) -2239825910784*a(n-18) -3795391531008*a(n-19) +11239750642176*a(n-20) +9072344881152*a(n-21) -37315540684800*a(n-22) -8727234969600*a(n-23) +78238462464000*a(n-24) -12303747072000*a(n-25) -93182607360000*a(n-26) +40370503680000*a(n-27) +47656304640000*a(n-28) -30098718720000*a(n-29).

%e Some solutions for n=3:

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

%e 1 1 0 0 1 3 5 0 6 3 3 1 1 1 3 3 5 3 6 1

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

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

%Y Column 4 of A234690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013