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.

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

Offset: 1

Author

R. H. Hardin Jul 04 2012

Keywords

• nonn
• tabl

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

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..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
		

Links

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

Crossrefs

Column 1 is A034494(n-1)

Column 2 is A001020(n-1)

Row 1 is A006342(n-1)

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)