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Number of nX1 0..7 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor
1

%I #5 Mar 31 2012 12:36:52

%S 1,8,64,372,1856,9052,45648,235538,1215616,6233356,31868448,163014678,

%T 834763824,4276077566,21900661172,112149148911,574278200480,

%U 2940790043388,15059692639376,77120252989206,394927990211792

%N Number of nX1 0..7 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor

%C Column 1 of A202916

%H R. H. Hardin, <a href="/A202909/b202909.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) -28*a(n-2) +84*a(n-3) -126*a(n-4) +252*a(n-5) -210*a(n-6) +330*a(n-7) -165*a(n-8) +220*a(n-9) -66*a(n-10) +78*a(n-11) -13*a(n-12) +14*a(n-13) -a(n-14) +a(n-15)

%e Some solutions for n=4

%e ..2....0....2....3....6....4....6....2....7....4....6....2....1....6....4....3

%e ..6....5....2....3....6....7....6....3....7....4....6....6....4....7....4....3

%e ..6....5....3....4....3....7....5....7....2....7....5....6....4....7....0....1

%e ..4....2....3....4....0....3....0....7....0....7....2....2....0....0....0....0

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 26 2011