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A274728 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

%I A274728 #4 Jul 03 2016 20:18:21
%S A274728 1,2,1,5,6,2,14,24,16,4,41,96,68,48,8,122,384,296,260,144,16,365,1536,
%T A274728 1300,1632,1040,432,32,1094,6144,5728,10368,9308,4132,1296,64,3281,
%U A274728 24576,25268,66132,84948,52912,16524,3888,128,9842,98304,111512,421904,771300
%N A274728 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.
%C A274728 Table starts
%C A274728 ...1.....2.......5.......14.........41..........122...........365
%C A274728 ...1.....6......24.......96........384.........1536..........6144
%C A274728 ...2....16......68......296.......1300.........5728.........25268
%C A274728 ...4....48.....260.....1632......10368........66132........421904
%C A274728 ...8...144....1040.....9308......84948.......771300.......7016284
%C A274728 ..16...432....4132....52912.....687248......8960464.....116633012
%C A274728 ..32..1296...16524...301784....5634776....105328812....1980677448
%C A274728 ..64..3888...66088..1721528...45990340...1237030912...33415073716
%C A274728 .128.11664..264332..9816048..375845052..14505195904..564905405336
%C A274728 .256.34992.1057316.55981988.3070055916.170291855288.9541460598408
%H A274728 R. H. Hardin, <a href="/A274728/b274728.txt">Table of n, a(n) for n = 1..220</a>
%F A274728 Empirical for column k:
%F A274728 k=1: a(n) = 2*a(n-1) for n>2
%F A274728 k=2: a(n) = 3*a(n-1) for n>3
%F A274728 k=3: a(n) = 3*a(n-1) +4*a(n-2) +a(n-3) -3*a(n-4) -4*a(n-5) for n>7
%F A274728 k=4: [order 8] for n>12
%F A274728 k=5: [order 15] for n>19
%F A274728 k=6: [order 30] for n>35
%F A274728 k=7: [order 59] for n>65
%F A274728 Empirical for row n:
%F A274728 n=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A274728 n=2: a(n) = 4*a(n-1) for n>2
%F A274728 n=3: a(n) = 6*a(n-1) -7*a(n-2) for n>3
%F A274728 n=4: a(n) = 8*a(n-1) -10*a(n-2) -4*a(n-3) +13*a(n-4) -7*a(n-5) +a(n-6) for n>7
%F A274728 n=5: [order 7] for n>9
%F A274728 n=6: [order 18] for n>20
%F A274728 n=7: [order 30] for n>34
%e A274728 Some solutions for n=4 k=4
%e A274728 ..0..1..1..2. .0..1..2..0. .0..1..2..2. .0..1..2..1. .0..1..2..1
%e A274728 ..1..0..2..0. .1..0..1..2. .1..0..1..0. .1..0..1..2. .1..0..1..0
%e A274728 ..0..2..0..2. .0..1..0..1. .2..1..0..1. .2..1..0..1. .0..1..0..1
%e A274728 ..2..0..2..1. .1..2..2..2. .1..2..1..2. .1..2..1..0. .1..2..1..2
%Y A274728 Column 1 is A000079(n-2).
%Y A274728 Row 1 is A007051(n-1).
%Y A274728 Row 2 is A002023(n-2).
%Y A274728 Row 3 is A235643(n-1).
%K A274728 nonn,tabl
%O A274728 1,2
%A A274728 _R. H. Hardin_, Jul 03 2016