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

Offset: 1

Author

R. H. Hardin Jul 05 2012

Keywords

• nonn
• tabl

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

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
..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
		

Links

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

Crossrefs

Column 1 is A198900

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)