A223255 T(n,k)=Two-loop graph coloring a rectangular array: number of nXk 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

5, 12, 12, 32, 52, 32, 80, 236, 236, 80, 208, 1076, 2172, 1076, 208, 528, 4908, 17828, 17828, 4908, 528, 1360, 22388, 166892, 307144, 166892, 22388, 1360, 3472, 102124, 1382228, 5359892, 5359892, 1382228, 102124, 3472, 8912, 465844, 12894316

Offset

1,1

Comments

Table starts

.....5......12.........32............80...............208..................528

....12......52........236..........1076..............4908................22388

....32.....236.......2172.........17828............166892..............1382228

....80....1076......17828........307144...........5359892.............93770308

...208....4908.....166892.......5359892.........200258884...........6581646956

...528...22388....1382228......93770308........6581646956.........465277782336

..1360..102124...12894316....1641741608......247417877452.......32969186423292

..3472..465844..107283636...28748561780.....8146965446276.....2337308796813336

..8912.2124972..996653548..503440061060...306270743418628...165726502883851820

.22800.9693172.8326150836.8816254627208.10089859264898796.11751198778793357708

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +4*a(n-2)

k=2: a(n) = 5*a(n-1) -2*a(n-2)

k=3: a(n) = 2*a(n-1) +75*a(n-2) -126*a(n-3) -70*a(n-4) +48*a(n-5)

k=4: a(n) = 20*a(n-1) -28*a(n-2) -299*a(n-3) +436*a(n-4) +476*a(n-5) -460*a(n-6) for n>7

k=5: [order 16]

k=6: [order 24] for n>25

k=7: [order 59]

Example

Some solutions for n=3 k=4
..1..0..3..4....0..1..2..1....0..1..0..1....2..0..4..0....0..1..0..3
..0..3..0..3....3..0..1..0....4..0..1..0....0..1..0..4....3..0..4..0
..1..0..2..0....0..1..0..1....0..2..0..2....2..0..1..0....0..1..0..1

Crossrefs

Column 1 is A183682(n-1)

Sequence in context: A259911 A259860 A268035 * A367573 A076537 A263580

Adjacent sequences: A223252 A223253 A223254 * A223256 A223257 A223258

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved