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A275228 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.

%I A275228 #4 Jul 20 2016 18:28:39
%S A275228 1,2,1,5,6,2,14,36,11,4,41,216,61,27,8,122,1296,339,187,66,16,365,
%T A275228 7776,1885,1302,648,162,32,1094,46656,10483,9075,6448,2282,404,64,
%U A275228 3281,279936,58301,63267,64248,32388,8134,1007,128,9842,1679616,324243,441090,640250
%N A275228 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.
%C A275228 Table starts
%C A275228 ...1....2......5.......14.........41.........122...........365............1094
%C A275228 ...1....6.....36......216.......1296........7776.........46656..........279936
%C A275228 ...2...11.....61......339.......1885.......10483.........58301..........324243
%C A275228 ...4...27....187.....1302.......9075.......63267........441090.........3075255
%C A275228 ...8...66....648.....6448......64248......640250.......6380362........63583084
%C A275228 ..16..162...2282....32388.....460034.....6534900......92831330......1318716132
%C A275228 ..32..404...8134...164645....3334854....67550874....1368326231.....27717164160
%C A275228 ..64.1007..29027...844176...24595019...716735348...20887845278....608741311725
%C A275228 .128.2512.103456..4319300..181187962..7605814181..319348056936..13409199459965
%C A275228 .256.6271.368889.22083548.1332436071.80496567059.4865299894416.294093896351121
%H A275228 R. H. Hardin, <a href="/A275228/b275228.txt">Table of n, a(n) for n = 1..180</a>
%F A275228 Empirical for column k:
%F A275228 k=1: a(n) = 2*a(n-1) for n>2
%F A275228 k=2: a(n) = 3*a(n-1) -a(n-2) -2*a(n-4) +a(n-5) for n>6
%F A275228 k=3: [order 9] for n>13
%F A275228 k=4: [order 31] for n>35
%F A275228 k=5: [order 81] for n>86
%F A275228 Empirical for row n:
%F A275228 n=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A275228 n=2: a(n) = 6*a(n-1)
%F A275228 n=3: a(n) = 7*a(n-1) -8*a(n-2)
%F A275228 n=4: a(n) = 9*a(n-1) -15*a(n-2) +6*a(n-3)
%F A275228 n=5: a(n) = 11*a(n-1) -9*a(n-2) -15*a(n-3) +20*a(n-4) -6*a(n-5) for n>6
%F A275228 n=6: a(n) = 19*a(n-1) -75*a(n-2) +101*a(n-3) -44*a(n-4) for n>5
%F A275228 n=7: a(n) = 20*a(n-1) +57*a(n-2) -1206*a(n-3) +3096*a(n-4) +2306*a(n-5) -16957*a(n-6) +20440*a(n-7) -7755*a(n-8) for n>9
%e A275228 Some solutions for n=4 k=4
%e A275228 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..2. .0..0..0..0
%e A275228 ..2..0..1..0. .1..0..1..0. .1..0..1..2. .1..0..2..0. .1..2..1..2
%e A275228 ..0..2..0..2. .2..1..0..1. .2..2..2..1. .2..1..0..2. .2..1..2..1
%e A275228 ..2..0..2..0. .1..2..2..0. .1..0..1..0. .1..0..2..0. .0..0..1..0
%Y A275228 Column 1 is A000079(n-2).
%Y A275228 Row 1 is A007051(n-1).
%Y A275228 Row 2 is A000400(n-1).
%Y A275228 Row 4 is A078100.
%K A275228 nonn,tabl
%O A275228 1,2
%A A275228 _R. H. Hardin_, Jul 20 2016