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%I #4 Nov 09 2013 06:52:07
%S 2,3,6,4,15,23,7,32,97,102,12,87,340,715,492,24,229,1598,4179,5643,
%T 2485,48,647,7429,33659,54868,46075,12858,103,1829,38713,265510,
%U 738459,741430,382341,67354,222,5293,203544,2308095,9796477,16471575,10145989,3196783
%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 antidiagonal neighbors, with values 0..3 introduced in row major order
%C Table starts
%C .......2.........3...........4.............7..............12.................24
%C .......6........15..........32............87.............229................647
%C ......23........97.........340..........1598............7429..............38713
%C .....102.......715........4179.........33659..........265510............2308095
%C .....492......5643.......54868........738459.........9796477..........144109697
%C ....2485.....46075......741430......16471575.......367351650.........9081622778
%C ...12858....382341....10145989.....370059818.....13839802182.......572792301557
%C ...67354...3196783...139597860....8337875579....522071407304.....36148438185936
%C ..355003..26821757..1925134584..188061528227..19702443415959...2281891799253071
%C .1876862.225400759.26574209688.4243377409271.743668294490912.144055012148018656
%H R. H. Hardin, <a href="/A231451/b231451.txt">Table of n, a(n) for n = 1..126</a>
%F Empirical for column k:
%F k=1: a(n) = 11*a(n-1) -41*a(n-2) +65*a(n-3) -43*a(n-4) +9*a(n-5)
%F k=2: [order 7]
%F k=3: [order 17]
%F k=4: [order 25]
%F k=5: [order 65]
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)
%F n=2: [order 16]
%F n=3: [order 50] for n>51
%e Some solutions for n=4 k=4
%e ..0..0..1..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..1
%e ..0..1..1..1..0....0..1..1..0..0....0..0..1..1..1....0..1..1..1..0
%e ..1..1..1..0..0....1..2..2..0..0....0..1..2..2..0....0..0..0..0..2
%e ..1..1..1..1..1....2..2..0..0..0....1..2..2..0..0....2..2..2..2..2
%e ..0..0..0..0..0....3..3..3..3..3....0..0..0..0..0....1..1..1..1..1
%Y Row 1 is A231337(n-1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 09 2013
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