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

1,3

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

Links

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

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)

Example

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

Crossrefs

Column 3 is A138977

Column 4 is A052934

Row 1 is A001045

Row 2 is A094554(n+1)

Sequence in context: A192787 A268724 A248569 * A286952 A100052 A128504

Adjacent sequences: A214098 A214099 A214100 * A214102 A214103 A214104

Keyword

nonn,tabl

Author

R. H. Hardin Jul 04 2012

Status

approved