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A276299 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.

%I A276299 #4 Aug 28 2016 08:27:29
%S A276299 1,1,2,2,4,5,4,12,11,14,8,36,45,31,41,16,108,173,189,88,122,32,324,
%T A276299 693,1017,805,250,365,64,972,2765,5909,5965,3437,710,1094,128,2916,
%U A276299 11061,33461,50949,34865,14693,2016,3281,256,8748,44237,191289,408105,442001
%N A276299 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.
%C A276299 Table starts
%C A276299 ....1.....1.......2........4..........8...........16............32
%C A276299 ....2.....4......12.......36........108..........324...........972
%C A276299 ....5....11......45......173........693.........2765.........11061
%C A276299 ...14....31.....189.....1017.......5909........33461........191289
%C A276299 ...41....88.....805.....5965......50949.......408105.......3363533
%C A276299 ..122...250....3437....34865.....442001......4988145......59728757
%C A276299 ..365...710...14693...203933....3861469.....61239977....1073114625
%C A276299 .1094..2016...62829..1192701...33851605....752660245...19398127957
%C A276299 .3281..5724..268677..6974781..297360321...9254592049..352134188049
%C A276299 .9842.16252.1148973.40786925.2615328377.113817204341.6411366745009
%H A276299 R. H. Hardin, <a href="/A276299/b276299.txt">Table of n, a(n) for n = 1..264</a>
%F A276299 Empirical for column k:
%F A276299 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A276299 k=2: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-3) for n>4
%F A276299 k=3: a(n) = 6*a(n-1) -8*a(n-2) +4*a(n-3) -7*a(n-4) +6*a(n-5) for n>7
%F A276299 k=4: [order 11] for n>13
%F A276299 k=5: [order 33] for n>37
%F A276299 k=6: [order 70] for n>75
%F A276299 Empirical for row n:
%F A276299 n=1: a(n) = 2*a(n-1) for n>2
%F A276299 n=2: a(n) = 3*a(n-1) for n>2
%F A276299 n=3: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) for n>4
%F A276299 n=4: a(n) = 4*a(n-1) +10*a(n-2) -6*a(n-4) -22*a(n-5) +15*a(n-6) for n>8
%F A276299 n=5: [order 15] for n>17
%F A276299 n=6: [order 30] for n>32
%F A276299 n=7: [order 59] for n>61
%e A276299 Some solutions for n=4 k=4
%e A276299 ..0..1..0..2. .0..1..2..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A276299 ..0..1..0..1. .2..1..2..1. .0..1..2..1. .0..1..0..1. .0..1..0..2
%e A276299 ..0..2..0..1. .2..1..2..0. .2..1..0..1. .2..1..2..1. .0..2..0..2
%e A276299 ..0..1..0..2. .0..1..2..0. .0..1..2..0. .0..1..0..1. .1..2..0..1
%Y A276299 Column 1 is A007051(n-1).
%Y A276299 Row 1 is A000079(n-2).
%Y A276299 Row 2 is A003946(n-1).
%K A276299 nonn,tabl
%O A276299 1,3
%A A276299 _R. H. Hardin_, Aug 28 2016