A275183 - OEIS

%I #4 Jul 19 2016 07:42:58

%S 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 141,85,37,32,1094,4096,1129,482,353,181,65,64,3281,16384,4021,1651,

%U 1465,914,389,114,128,9842,65536,14321,5653,6081,4603,2386,834,200,256,29525

%N 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 Table starts

%C ...1...2....5....14.....41.....122......365......1094.......3281........9842

%C ...1...4...16....64....256....1024.....4096.....16384......65536......262144

%C ...2...7...25....89....317....1129.....4021.....14321......51005......181657

%C ...4..12...41...141....482....1651.....5653.....19356......66277......226937

%C ...8..21...85...353...1465....6081....25241....104769.....434873.....1805057

%C ..16..37..181...914...4603...23313...117916....596625....3018913....15274618

%C ..32..65..389..2386..14643...90793...561044...3472521...21488129...132962186

%C ..64.114..834..6228..46799..355258..2688402..20397794..154665843..1172975241

%C .128.200.1781.16249.149772.1392050.12931103.120384453.1120217646.10428404709

%C .256.351.3799.42451.479722.5466938.62408531.713359905.8156812360.93298660085

%H R. H. Hardin, <a href="/A275183/b275183.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) for n>2

%F k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3)

%F 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 k=4: [order 9] for n>12

%F k=5: [order 16] for n>21

%F k=6: [order 34] for n>39

%F k=7: [order 67] for n>73

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -3*a(n-2)

%F n=2: a(n) = 4*a(n-1)

%F n=3: a(n) = 3*a(n-1) +2*a(n-2)

%F n=4: a(n) = 2*a(n-1) +4*a(n-2) +3*a(n-3) for n>4

%F n=5: a(n) = 2*a(n-1) +7*a(n-2) +8*a(n-3) for n>5

%F 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 n=7: [order 9] for n>10

%e Some solutions for n=4 k=4

%e ..0..0..1..2. .0..1..1..2. .0..0..1..1. .0..0..1..2. .0..0..0..1

%e ..2..2..0..1. .2..0..0..1. .2..2..0..0. .2..2..0..1. .1..2..2..0

%e ..0..1..2..0. .1..2..2..2. .0..1..1..2. .1..1..2..2. .0..1..1..2

%e ..2..0..1..2. .0..0..1..1. .2..0..0..1. .0..0..0..1. .2..2..0..0

%Y Column 1 is A000079(n-2).

%Y Column 2 is A005251(n+3).

%Y Row 1 is A007051(n-1).

%Y Row 2 is A000302(n-1).

%Y Row 3 is A007484(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 19 2016