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.

1, 2, 1, 5, 4, 2, 14, 16, 7, 4, 41, 64, 25, 12, 8, 122, 256, 89, 41, 21, 16, 365, 1024, 317, 141, 85, 37, 32, 1094, 4096, 1129, 482, 353, 181, 65, 64, 3281, 16384, 4021, 1651, 1465, 914, 389, 114, 128, 9842, 65536, 14321, 5653, 6081, 4603, 2386, 834, 200, 256, 29525

Offset: 1

Author

R. H. Hardin, Jul 19 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

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

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

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

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

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

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

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

.128.200.1781.16249.149772.1392050.12931103.120384453.1120217646.10428404709

.256.351.3799.42451.479722.5466938.62408531.713359905.8156812360.93298660085

Examples

			Some solutions for n=4 k=4
..0..0..1..2. .0..1..1..2. .0..0..1..1. .0..0..1..2. .0..0..0..1
..2..2..0..1. .2..0..0..1. .2..2..0..0. .2..2..0..1. .1..2..2..0
..0..1..2..0. .1..2..2..2. .0..1..1..2. .1..1..2..2. .0..1..1..2
..2..0..1..2. .0..0..1..1. .2..0..0..1. .0..0..0..1. .2..2..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..364

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A005251(n+3).

Row 1 is A007051(n-1).

Row 2 is A000302(n-1).

Row 3 is A007484(n-1).

Formula

Empirical for column k:

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

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

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

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

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

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

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

Empirical for row n:

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

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

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

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

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

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

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