A223599 - OEIS

A223599

T(n,k)=Petersen graph (8,2) coloring a rectangular array: number of nXk 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph

16, 48, 256, 144, 256, 4096, 432, 1504, 1376, 65536, 1296, 6736, 16192, 7424, 1048576, 3888, 32768, 122608, 176224, 40160, 16777216, 11664, 156592, 1124064, 2372080, 1931968, 217600, 268435456, 34992, 755200, 9902320, 43725920, 47659632

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Table starts

............16........48..........144.............432...............1296

...........256.......256.........1504............6736..............32768

..........4096......1376........16192..........122608............1124064

.........65536......7424.......176224.........2372080...........43725920

.......1048576.....40160......1931968........47659632.........1807461152

......16777216....217600.....21308000.......982848688........77164934624

.....268435456...1180256....236213312.....20631729648......3355919411936

....4294967296...6405888...2629972704....438231627440....147579242411936

...68719476736..34782688..29389265856...9379905920496...6534353238114336

.1099511627776.188912640.329426847840.201754894742320.290550417324168160

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..161

FORMULA

Empirical for column k:

k=1: a(n) = 16*a(n-1)

k=2: a(n) = 8*a(n-1) -11*a(n-2) -16*a(n-3)

k=3: a(n) = 23*a(n-1) -153*a(n-2) +217*a(n-3) +258*a(n-4) -456*a(n-5) -104*a(n-6) +192*a(n-7)

k=4: [order 9]

k=5: [order 29]

k=6: [order 55]

Empirical for row n:

n=1: a(n) = 3*a(n-1)

n=2: a(n) = 6*a(n-1) +3*a(n-2) -42*a(n-3) -8*a(n-4) +48*a(n-5) for n>6

n=3: [order 11] for n>12

n=4: [order 28] for n>29

n=5: [order 74] for n>75

EXAMPLE

Some solutions for n=3 k=4

.14..6..5.13...13.15..9.15...12..4.12.10....6..5.13.15....8.14..8.10

..7..6..5..6...13.15..9..1...12..4.12..4....6..5.13..5....8.14..8.14

..5..6.14..6....9.15..9.11....5..4.12.14...13..5..6..5....6.14..6.14

CROSSREFS

Column 1 is A001025

Column 2 is A223434

Row 1 is A188825(n+1)

Sequence in context: A109098 A223395 A202329 * A223692 A165115 A165117

Adjacent sequences: A223596 A223597 A223598 * A223600 A223601 A223602

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 23 2013

STATUS

approved