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A275183 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

%I A275183 #4 Jul 19 2016 07:42:58
%S A275183 1,2,1,5,4,2,14,16,7,4,41,64,25,12,8,122,256,89,41,21,16,365,1024,317,
%T A275183 141,85,37,32,1094,4096,1129,482,353,181,65,64,3281,16384,4021,1651,
%U A275183 1465,914,389,114,128,9842,65536,14321,5653,6081,4603,2386,834,200,256,29525
%N A275183 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.
%C A275183 Table starts
%C A275183 ...1...2....5....14.....41.....122......365......1094.......3281........9842
%C A275183 ...1...4...16....64....256....1024.....4096.....16384......65536......262144
%C A275183 ...2...7...25....89....317....1129.....4021.....14321......51005......181657
%C A275183 ...4..12...41...141....482....1651.....5653.....19356......66277......226937
%C A275183 ...8..21...85...353...1465....6081....25241....104769.....434873.....1805057
%C A275183 ..16..37..181...914...4603...23313...117916....596625....3018913....15274618
%C A275183 ..32..65..389..2386..14643...90793...561044...3472521...21488129...132962186
%C A275183 ..64.114..834..6228..46799..355258..2688402..20397794..154665843..1172975241
%C A275183 .128.200.1781.16249.149772.1392050.12931103.120384453.1120217646.10428404709
%C A275183 .256.351.3799.42451.479722.5466938.62408531.713359905.8156812360.93298660085
%H A275183 R. H. Hardin, <a href="/A275183/b275183.txt">Table of n, a(n) for n = 1..364</a>
%F A275183 Empirical for column k:
%F A275183 k=1: a(n) = 2*a(n-1) for n>2
%F A275183 k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A275183 k=3: a(n) = 4*a(n-1) -6*a(n-2) +5*a(n-3) -a(n-4) -a(n-5) for n>8
%F A275183 k=4: [order 9] for n>12
%F A275183 k=5: [order 16] for n>21
%F A275183 k=6: [order 34] for n>39
%F A275183 k=7: [order 67] for n>73
%F A275183 Empirical for row n:
%F A275183 n=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A275183 n=2: a(n) = 4*a(n-1)
%F A275183 n=3: a(n) = 3*a(n-1) +2*a(n-2)
%F A275183 n=4: a(n) = 2*a(n-1) +4*a(n-2) +3*a(n-3) for n>4
%F A275183 n=5: a(n) = 2*a(n-1) +7*a(n-2) +8*a(n-3) for n>5
%F A275183 n=6: a(n) = 2*a(n-1) +12*a(n-2) +19*a(n-3) -4*a(n-4) -12*a(n-5) -16*a(n-6) for n>7
%F A275183 n=7: [order 9] for n>10
%e A275183 Some solutions for n=4 k=4
%e A275183 ..0..0..1..2. .0..1..1..2. .0..0..1..1. .0..0..1..2. .0..0..0..1
%e A275183 ..2..2..0..1. .2..0..0..1. .2..2..0..0. .2..2..0..1. .1..2..2..0
%e A275183 ..0..1..2..0. .1..2..2..2. .0..1..1..2. .1..1..2..2. .0..1..1..2
%e A275183 ..2..0..1..2. .0..0..1..1. .2..0..0..1. .0..0..0..1. .2..2..0..0
%Y A275183 Column 1 is A000079(n-2).
%Y A275183 Column 2 is A005251(n+3).
%Y A275183 Row 1 is A007051(n-1).
%Y A275183 Row 2 is A000302(n-1).
%Y A275183 Row 3 is A007484(n-1).
%K A275183 nonn,tabl
%O A275183 1,2
%A A275183 _R. H. Hardin_, Jul 19 2016