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Number of nX5 0..2 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #4 Dec 22 2016 12:52:24

%S 8,18,43,156,601,2006,7383,25400,89693,315334,1103371,3871860,

%T 13540353,47310262,165104587,575109252,2000994373,6951376238,

%U 24117548401,83567966688,289210301055,999751444526,3452205326385,11908457582008

%N Number of nX5 0..2 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 5 of A279902.

%H R. H. Hardin, <a href="/A279899/b279899.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +16*a(n-2) -56*a(n-3) -146*a(n-4) +316*a(n-5) +814*a(n-6) -868*a(n-7) -2325*a(n-8) +1214*a(n-9) +2214*a(n-10) -1932*a(n-11) +3703*a(n-12) +4994*a(n-13) -12996*a(n-14) -3398*a(n-15) +12908*a(n-16) -8904*a(n-17) +2591*a(n-18) +12692*a(n-19) -11884*a(n-20) -3456*a(n-21) +4880*a(n-22) +192*a(n-23) -576*a(n-24) for n>27

%e Some solutions for n=4

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

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

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

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

%Y Cf. A279902.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 22 2016