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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order
7

%I #4 Nov 07 2013 18:16:20

%S 3,4,4,7,9,7,12,22,22,12,24,59,96,59,24,48,159,453,453,159,48,103,439,

%T 2302,3572,2302,439,103,222,1236,12052,30269,30269,12052,1236,222,493,

%U 3527,65326,259011,465033,259011,65326,3527,493,1100,10184,358429

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order

%C Table starts

%C ....3.....4........7........12.........24.........48........103..........222

%C ....4.....9.......22........59........159........439.......1236.........3527

%C ....7....22.......96.......453.......2302......12052......65326.......358429

%C ...12....59......453......3572......30269.....259011....2278003.....20081717

%C ...24...159.....2302.....30269.....465033....6871838..105988195...1613424264

%C ...48...439....12052....259011....6871838..169968099.4400551358.111907856129

%C ..103..1236....65326...2278003..105988195.4400551358

%C ..222..3527...358429..20081717.1613424264

%C ..493.10184..1989453.178468093

%C .1100.29679.11087559

%H R. H. Hardin, <a href="/A231343/b231343.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)

%F k=2: a(n) = 5*a(n-1) -6*a(n-2) +2*a(n-3) -8*a(n-4) +6*a(n-5) -a(n-6) +3*a(n-7)

%F k=3: [order 34]

%F k=4: [order 97] for n>98

%e Some solutions for n=4 k=4

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

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

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

%e ..3..3..2..2..2....2..2..2..2..1....2..2..2..0..0....0..2..2..0..0

%e ..3..3..2..2..2....2..2..2..2..1....3..3..3..3..3....0..2..2..2..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 07 2013