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

%I #6 Jun 20 2022 19:44:01

%S 15008,37352,94432,274520,808160,2646344,8731840,31384136,113059808,

%T 437774312,1689860992,6944469320,28298174240,121873410344,

%U 517811131840,2312599876616,10141883194208,46569251868392,209116100618752

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

%H R. H. Hardin, <a href="/A234654/b234654.txt">Table of n, a(n) for n = 1..169</a>

%F Empirical: a(n) = 8*a(n-1) +85*a(n-2) -820*a(n-3) -2645*a(n-4) +35720*a(n-5) +27415*a(n-6) -866260*a(n-7) +408982*a(n-8) +12858104*a(n-9) -16068980*a(n-10) -120659920*a(n-11) +221967320*a(n-12) +709627680*a(n-13) -1711158240*a(n-14) -2457267840*a(n-15) +7901564544*a(n-16) +4009471488*a(n-17) -21498324480*a(n-18) +987863040*a(n-19) +31468953600*a(n-20) -12541132800*a(n-21) -18911232000*a(n-22) +11943936000*a(n-23).

%e Some solutions for n=3:

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

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

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

%e 5 5 5 1 4 0 4 0 4 1 5 1 4 5 5 1 5 1 0 0

%Y Column 4 of A234658.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2013