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Number of (n+1)X(4+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor
1

%I #4 Nov 21 2013 06:18:42

%S 1287,96999,7258599,544777651,40896843985,3070212041183,

%T 230487644229167,17303223331864431,1298991725349537089,

%U 97518218023627044295,7320911028394527687575,549597186787143997790315

%N Number of (n+1)X(4+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor

%C Column 4 of A232257

%H R. H. Hardin, <a href="/A232253/b232253.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 69*a(n-1) +555*a(n-2) -7271*a(n-3) -16398*a(n-4) +266152*a(n-5) -265357*a(n-6) -2539887*a(n-7) -7724280*a(n-8) -6811008*a(n-9) +16331136*a(n-10) +18397456*a(n-11) -13469384*a(n-12) -10822060*a(n-13) +6278955*a(n-14) +1333583*a(n-15) -1195787*a(n-16) +285229*a(n-17) -45161*a(n-18) +3471*a(n-19) -6*a(n-20) -6*a(n-21)

%e Some solutions for n=2

%e ..1..1..0..2..2....2..2..1..0..0....0..0..0..0..1....2..2..1..1..2

%e ..1..0..1..2..1....1..0..2..2..2....2..2..2..2..2....2..2..1..2..2

%e ..2..2..2..1..1....0..0..1..1..1....2..2..2..0..0....2..0..0..0..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 21 2013