A214166 T(n,k)=Number of 0..5 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..5 introduced in row major order

1, 1, 4, 4, 18, 34, 11, 337, 902, 481, 41, 5994, 88261, 60320, 8731, 161, 121778, 7386816, 27240856, 4242606, 174454, 694, 2518082, 655418810, 9601970064, 8548472292, 300785428, 3603244, 3151, 52655411, 57661437162, 3598372134742

Offset

1,3

Comments

Table starts

....1.......1..........4.............11................41..................161

....4......18........337...........5994............121778..............2518082

...34.....902......88261........7386816.........655418810..........57661437162

..481...60320...27240856.....9601970064.....3598372134742.....1329144373535118

.8731.4242606.8548472292.12515731371696.19767477649307133.30641183868207736684

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

k=1: a(n) = 32*a(n-1) -262*a(n-2) +672*a(n-3) -441*a(n-4)

k=2: a(n) = 84*a(n-1) -945*a(n-2) +1562*a(n-3)

k=3: a(n) = 370*a(n-1) -18411*a(n-2) +297448*a(n-3) -1839799*a(n-4) +4424682*a(n-5) -4113757*a(n-6) +1249468*a(n-7)

k=4: a(n) = 1402*a(n-1) -130492*a(n-2) +2979072*a(n-3) -15573492*a(n-4) +12571416*a(n-5)

k=5: (order 15)

Empirical for row n:

n=1: a(k)=10*a(k-1)-30*a(k-2)+20*a(k-3)+31*a(k-4)-30*a(k-5)

n=2: a(k)=21*a(k-1)+49*a(k-2)-959*a(k-3)-1869*a(k-4)+7679*a(k-5)+15051*a(k-6)-6741*a(k-7)-13230*a(k-8)

n=3: (order 22)

n=4: (order 60)

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..2....1..2....1..2....1..2....1..2....1..0....1..0....1..0....2..3....2..3
..3..4....0..1....3..0....2..0....0..3....2..1....2..3....2..3....3..1....0..1
..5..3....1..0....0..4....0..2....1..2....0..2....0..4....1..0....4..2....1..3

Crossrefs

Column 1 is A198900

Sequence in context: A128090 A119948 A005222 * A214187 A214238 A133039

Adjacent sequences: A214163 A214164 A214165 * A214167 A214168 A214169

Keyword

nonn,tabl

Author

R. H. Hardin Jul 05 2012

Status

approved