A214101 T(n,k)=Number of 0..2 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..2 introduced in row major order.

1, 1, 3, 3, 2, 9, 5, 19, 4, 27, 11, 30, 121, 8, 81, 21, 143, 180, 771, 16, 243, 43, 322, 2041, 1080, 4913, 32, 729, 85, 1179, 5068, 29540, 6480, 31307, 64, 2187, 171, 3110, 37441, 79968, 428383, 38880, 199497, 128, 6561, 341, 10183, 121588, 1241355, 1262128

Offset: 1

Author

R. H. Hardin Jul 04 2012

Keywords

• nonn
• tabl

Comments

Table starts

..1..1....3....5.....11......21.......43........85........171.........341

..3..2...19...30....143.....322.....1179......3110......10183.......28842

..9..4..121..180...2041....5068....37441....121588.....722009.....2720828

.27..8..771.1080..29540...79968..1241355...4807928...54733587...263068168

.81.16.4913.6480.428383.1262128.41634729.190532944.4254090231.25595530224

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..309

Crossrefs

Column 3 is A138977

Column 4 is A052934

Row 1 is A001045

Row 2 is A094554(n+1)

Formula

Empirical for column k:

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

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

k=3: a(n) = 7*a(n-1) -4*a(n-2)

k=4: a(n) = 6*a(n-1)

k=5: a(n) = 19*a(n-1) -71*a(n-2) +86*a(n-3) -24*a(n-4)

k=6: a(n) = 18*a(n-1) -36*a(n-2) +16*a(n-3)

k=7: a(n) = 54*a(n-1) -820*a(n-2) +4906*a(n-3) -11803*a(n-4) +11888*a(n-5) -4672*a(n-6) +576*a(n-7)

Empirical for row n:

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

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

n=3: a(k)=3*a(k-1)+15*a(k-2)-33*a(k-3)-22*a(k-4)+38*a(k-5)+8*a(k-6)-8*a(k-7)

n=4: (order 11)

n=5: (order 29)

n=6: (order 40)