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

Author

R. H. Hardin, Dec 06 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A006367(n-1).

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