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

Author

R. H. Hardin, Jul 20 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-2).

Row 1 is A007051(n-1).

Row 2 is A000400(n-1).

Row 4 is A078100.

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