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A279158 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 7
0, 0, 0, 2, 0, 2, 2, 4, 4, 2, 5, 12, 20, 12, 5, 8, 30, 72, 72, 30, 8, 15, 72, 255, 428, 255, 72, 15, 26, 162, 874, 2294, 2294, 874, 162, 26, 46, 356, 2903, 11932, 20104, 11932, 2903, 356, 46, 80, 766, 9336, 60304, 166552, 166552, 60304, 9336, 766, 80, 139, 1616, 29578 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

..0....0.....2.......2.........5...........8............15..............26

..0....0.....4......12........30..........72...........162.............356

..2....4....20......72.......255.........874..........2903............9336

..2...12....72.....428......2294.......11932.........60304..........297092

..5...30...255....2294.....20104......166552.......1331471........10508084

..8...72...874...11932....166552.....2145788......26724386.......330704288

.15..162..2903...60304...1331471....26724386.....517476726.....10025433990

.26..356..9336..297092..10508084...330704288...10025433990....305617345164

.46..766.29578.1443498..81594334..4027185426..191191601644...9168921176076

.80.1616.92528.6930508.624717186.48341053840.3592564336954.270873567300596

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -12*a(n-4) +8*a(n-5) -4*a(n-6) +8*a(n-7)

k=3: [order 22] for n>23

k=4: [order 56] for n>57

EXAMPLE

Some solutions for n=4 k=4

..0..1..0..1. .0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..0

..0..0..1..0. .0..0..1..0. .1..0..1..1. .0..1..0..1. .0..0..1..1

..1..1..0..1. .1..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..0..0

..0..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..0..1. .0..1..0..1

CROSSREFS

Column 1 is A006367(n-1).

Sequence in context: A181346 A300815 A002121 * A273166 A331262 A300822

Adjacent sequences:  A279155 A279156 A279157 * A279159 A279160 A279161

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 06 2016

STATUS

approved

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)