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.

1, 2, 1, 5, 6, 2, 14, 36, 11, 4, 41, 216, 61, 27, 8, 122, 1296, 339, 187, 66, 16, 365, 7776, 1885, 1302, 648, 162, 32, 1094, 46656, 10483, 9075, 6448, 2282, 404, 64, 3281, 279936, 58301, 63267, 64248, 32388, 8134, 1007, 128, 9842, 1679616, 324243, 441090, 640250

Offset

1,2

Comments

Table starts

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

...1....6.....36......216.......1296........7776.........46656..........279936

...2...11.....61......339.......1885.......10483.........58301..........324243

...4...27....187.....1302.......9075.......63267........441090.........3075255

...8...66....648.....6448......64248......640250.......6380362........63583084

..16..162...2282....32388.....460034.....6534900......92831330......1318716132

..32..404...8134...164645....3334854....67550874....1368326231.....27717164160

..64.1007..29027...844176...24595019...716735348...20887845278....608741311725

.128.2512.103456..4319300..181187962..7605814181..319348056936..13409199459965

.256.6271.368889.22083548.1332436071.80496567059.4865299894416.294093896351121

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -a(n-2) -2*a(n-4) +a(n-5) for n>6

k=3: [order 9] for n>13

k=4: [order 31] for n>35

k=5: [order 81] for n>86

Empirical for row n:

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

n=2: a(n) = 6*a(n-1)

n=3: a(n) = 7*a(n-1) -8*a(n-2)

n=4: a(n) = 9*a(n-1) -15*a(n-2) +6*a(n-3)

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

n=6: a(n) = 19*a(n-1) -75*a(n-2) +101*a(n-3) -44*a(n-4) for n>5

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

Example

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

Crossrefs

Column 1 is A000079(n-2).

Row 1 is A007051(n-1).

Row 2 is A000400(n-1).

Row 4 is A078100.

Sequence in context: A274728 A062991 A234950 * A118984 A073474 A067311

Adjacent sequences: A275225 A275226 A275227 * A275229 A275230 A275231

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 20 2016

Status

approved