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A214112 T(n,k)=Number of 0..3 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..3 introduced in row major order 12
1, 1, 4, 4, 11, 25, 10, 111, 121, 172, 31, 670, 3502, 1331, 1201, 91, 4994, 44900, 110985, 14641, 8404, 274, 34041, 825105, 3008980, 3517864, 161051, 58825, 820, 241021, 12777541, 136579852, 201647240, 111505491, 1771561, 411772, 2461, 1678940 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

....1.....1.......4........10..........31............91.............274

....4....11.....111.......670........4994.........34041..........241021

...25...121....3502.....44900......825105......12777541.......214404272

..172..1331..110985...3008980...136579852....4797577911....191154162535

.1201.14641.3517864.201647240.22615881851.1801391900581.170522196557894

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..160

FORMULA

Empirical for column k:

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

k=2: a(n) = 11*a(n-1)

k=3: a(n) = 35*a(n-1) -107*a(n-2) +73*a(n-3)

k=4: a(n) = 68*a(n-1) -66*a(n-2)

k=5: a(n) = 200*a(n-1) -5769*a(n-2) +11744*a(n-3) +43057*a(n-4) -89856*a(n-5) +40625*a(n-6)

k=6: a(n) = 416*a(n-1) -15454*a(n-2) +89758*a(n-3) +90848*a(n-4) -438718*a(n-5) +62801*a(n-6)

k=7: (order 15)

Empirical for row n:

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

n=2: a(k)=4*a(k-1)+22*a(k-2)-4*a(k-3)-21*a(k-4)

n=3: a(k)=11*a(k-1)+123*a(k-2)-509*a(k-3)-1615*a(k-4)+7137*a(k-5)-19*a(k-6)-20571*a(k-7)+13176*a(k-8)+13932*a(k-9)-11664*a(k-10)

n=4: (order 26)

n=5: (order 71)

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

..1..0....1..2....2..3....1..0....1..0....1..0....1..2....1..0....1..0....1..2

..0..1....0..1....3..1....0..1....2..3....2..1....3..0....0..2....2..3....3..1

..1..2....1..0....1..0....1..0....3..2....3..0....0..1....1..3....3..1....0..2

CROSSREFS

Column 1 is A034494(n-1)

Column 2 is A001020(n-1)

Row 1 is A006342(n-1)

Sequence in context: A302516 A254205 A048223 * A211950 A014012 A273391

Adjacent sequences:  A214109 A214110 A214111 * A214113 A214114 A214115

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jul 04 2012

STATUS

approved

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Last modified November 15 19:18 EST 2019. Contains 329149 sequences. (Running on oeis4.)