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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 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)