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

1,2

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

Links

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

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

Example

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

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).

Sequence in context: A359131 A164678 A164679 * A275131 A280513 A185023

Adjacent sequences: A275180 A275181 A275182 * A275184 A275185 A275186

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 19 2016

Status

approved