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A276248 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-2) and new values introduced in order 0..2.

%I A276248 #4 Aug 25 2016 11:04:11
%S A276248 1,2,2,3,9,5,6,24,36,14,12,72,85,144,41,24,216,279,347,576,122,48,648,
%T A276248 900,1447,1404,2304,365,96,1944,2837,6372,7316,5671,9216,1094,192,
%U A276248 5832,9148,26325,43662,36744,23000,36864,3281,384,17496,29570,115682,234431
%N A276248 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-2) and new values introduced in order 0..2.
%C A276248 Table starts
%C A276248 ....1......2.......3........6........12..........24...........48.............96
%C A276248 ....2......9......24.......72.......216.........648.........1944...........5832
%C A276248 ....5.....36......85......279.......900........2837.........9148..........29570
%C A276248 ...14....144.....347.....1447......6372.......26325.......115682.........509750
%C A276248 ...41....576....1404.....7316.....43662......234431......1423062........8496628
%C A276248 ..122...2304....5671....36744....291113.....2069454.....17450554......141165944
%C A276248 ..365...9216...23000...188696...2003694....18671229....219977330.....2410124377
%C A276248 .1094..36864...93204...966555..13727745...167951009...2780927371....41132001645
%C A276248 .3281.147456..377421..4951790..93489265..1509288801..35144231606...700435484735
%C A276248 .9842.589824.1529844.25428687.640009243.13609728840.446083313365.11973407175492
%H A276248 R. H. Hardin, <a href="/A276248/b276248.txt">Table of n, a(n) for n = 1..241</a>
%F A276248 Empirical for column k:
%F A276248 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A276248 k=2: a(n) = 4*a(n-1) for n>2
%F A276248 k=3: a(n) = 5*a(n-1) -4*a(n-2) +17*a(n-3) -83*a(n-4) +54*a(n-5) +56*a(n-6) for n>9
%F A276248 k=4: [order 36] for n>37
%F A276248 k=5: [order 41] for n>45
%F A276248 Empirical for row n:
%F A276248 n=1: a(n) = 2*a(n-1) for n>3
%F A276248 n=2: a(n) = 3*a(n-1) for n>3
%F A276248 n=3: [order 14] for n>15
%F A276248 n=4: [order 57] for n>60
%e A276248 Some solutions for n=4 k=4
%e A276248 ..0..0..1..1. .0..0..1..2. .0..0..1..1. .0..1..1..2. .0..0..1..2
%e A276248 ..1..2..2..1. .2..0..0..1. .2..2..0..1. .2..2..0..0. .2..2..0..1
%e A276248 ..0..1..2..2. .1..1..2..2. .0..1..2..2. .1..1..2..2. .1..1..2..2
%e A276248 ..2..0..0..1. .0..0..1..2. .0..0..1..1. .2..0..1..1. .2..0..0..2
%Y A276248 Column 1 is A007051(n-1).
%Y A276248 Column 2 is A002063(n-2).
%Y A276248 Row 1 is A003945(n-2).
%K A276248 nonn,tabl
%O A276248 1,2
%A A276248 _R. H. Hardin_, Aug 25 2016