A214141 - OEIS

A214141

T(n,k)=Number of 0..4 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..4 introduced in row major order

1, 1, 4, 4, 17, 33, 11, 257, 514, 380, 40, 3074, 28278, 16388, 4801, 147, 40434, 1101051, 3221873, 524296, 62004, 568, 522515, 47730973, 396246659, 367793014, 16777232, 804833, 2227, 6800539, 2000093424, 56449101747, 142612676441, 41989913081

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

OFFSET

1,3

COMMENTS

Table starts

....1......1.........4...........11.............40...............147

....4.....17.......257.........3074..........40434............522515

...33....514.....28278......1101051.......47730973........2000093424

..380..16388...3221873....396246659....56449101747.....7658621867351

.4801.524296.367793014.142612676441.66761857485037.29325981412599886

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..111

FORMULA

Empirical for column k:

k=1: a(n) = 17*a(n-1) -55*a(n-2) +39*a(n-3)

k=2: a(n) = 34*a(n-1) -64*a(n-2)

k=3: a(n) = 129*a(n-1) -1759*a(n-2) +7575*a(n-3) -9064*a(n-4) +3120*a(n-5)

k=4: a(n) = 373*a(n-1) -4754*a(n-2) +15312*a(n-3)

k=5: (order 10)

k=6: (order 9)

Empirical for row n:

n=1: a(k)=6*a(k-1)-7*a(k-2)-6*a(k-3)+8*a(k-4)

n=2: a(k)=10*a(k-1)+50*a(k-2)-116*a(k-3)-361*a(k-4)+106*a(k-5)+312*a(k-6)

n=3: (order 15)

n=4: (order 37)

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

..3..2....2..0....2..3....2..1....0..4....2..3....3..2....2..3....1..4....0..1

..4..0....3..4....1..0....1..2....1..0....0..4....2..0....3..4....4..3....1..3

CROSSREFS

Column 1 is A198900

Sequence in context: A117785 A117787 A113727 * A193961 A368197 A205110

Adjacent sequences: A214138 A214139 A214140 * A214142 A214143 A214144

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jul 05 2012

STATUS

approved