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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A076537 A263580 A110134

Adjacent sequences:  A223252 A223253 A223254 * A223256 A223257 A223258

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 18 2013

STATUS

approved

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Last modified September 15 04:28 EDT 2019. Contains 327062 sequences. (Running on oeis4.)