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

Author

R. H. Hardin Jul 05 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A198900

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) [phone]*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)