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A275142 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

%I A275142 #4 Jul 17 2016 16:26:26
%S A275142 1,1,2,2,6,5,4,16,36,14,8,48,80,216,41,16,144,224,400,1296,122,32,432,
%T A275142 528,1088,2000,7776,365,64,1296,1216,2320,5248,10000,46656,1094,128,
%U A275142 3888,2816,6464,9744,25344,50000,279936,3281,256,11664,6544,17872,32384,41360
%N A275142 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.
%C A275142 Table starts
%C A275142 ....1........1.......2........4........8........16........32.........64
%C A275142 ....2........6......16.......48......144.......432......1296.......3888
%C A275142 ....5.......36......80......224......528......1216......2816.......6544
%C A275142 ...14......216.....400.....1088.....2320......6464.....17872......49792
%C A275142 ...41.....1296....2000.....5248.....9744.....32384....107472.....362176
%C A275142 ..122.....7776...10000....25344....41360....165568....663904....2695808
%C A275142 ..365....46656...50000...122368...175120....841536...4055152...19906560
%C A275142 .1094...279936..250000...590848...741904...4283968..24875600..147762240
%C A275142 .3281..1679616.1250000..2852864..3142672..21800000.152379136.1093999424
%C A275142 .9842.10077696.6250000.13774848.13312656.110943552.933805200.8109111360
%H A275142 R. H. Hardin, <a href="/A275142/b275142.txt">Table of n, a(n) for n = 1..721</a>
%F A275142 Empirical for column k:
%F A275142 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A275142 k=2: a(n) = 6*a(n-1)
%F A275142 k=3: a(n) = 5*a(n-1) for n>2
%F A275142 k=4: a(n) = 4*a(n-1) +4*a(n-2) for n>3
%F A275142 k=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3) for n>4
%F A275142 k=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>6
%F A275142 k=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>7
%F A275142 Empirical for row n:
%F A275142 n=1: a(n) = 2*a(n-1) for n>2
%F A275142 n=2: a(n) = 3*a(n-1) for n>3
%F A275142 n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>5
%F A275142 n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>9
%F A275142 n=5: [order 8] for n>12
%F A275142 n=6: [order 13] for n>18
%F A275142 n=7: [order 21] for n>27
%e A275142 Some solutions for n=5 k=4
%e A275142 ..0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..2..1. .0..1..2..0
%e A275142 ..2..0..1..0. .0..2..1..2. .2..0..1..2. .2..0..2..0. .0..1..2..0
%e A275142 ..2..0..1..2. .1..2..1..0. .1..2..1..2. .2..0..1..2. .2..0..2..0
%e A275142 ..1..2..0..1. .0..1..2..1. .0..2..0..1. .2..0..1..2. .2..0..1..2
%e A275142 ..0..2..0..1. .2..1..2..0. .0..1..2..0. .1..2..0..2. .0..1..0..1
%Y A275142 Column 1 is A007051(n-1).
%Y A275142 Column 2 is A000400(n-1).
%Y A275142 Column 3 is A055842.
%Y A275142 Row 1 is A000079(n-2).
%K A275142 nonn,tabl
%O A275142 1,3
%A A275142 _R. H. Hardin_, Jul 17 2016