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.

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

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: A300815 A358933 A002121 * A273166 A331262 A300822

Adjacent sequences: A279155 A279156 A279157 * A279159 A279160 A279161

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 06 2016

Status

approved