A281888 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 638, 638, 0, 0, 0, 0, 4832, 9284, 4832, 0, 0, 0, 0, 35002, 112320, 112320, 35002, 0, 0, 0, 0, 241209, 1282388, 2156646, 1282388, 241209, 0, 0, 0, 0, 1612568, 13907664, 38763782, 38763782, 13907664, 1612568, 0, 0

Offset

1,13

Comments

Table starts

.0.0........0...........0.............0...............0.................0

.0.0........0...........0.............0...............0.................0

.0.0.......68.........638..........4832...........35002............241209

.0.0......638........9284........112320.........1282388..........13907664

.0.0.....4832......112320.......2156646........38763782.........663476572

.0.0....35002.....1282388......38763782......1091754188.......29340232714

.0.0...241209....13907664.....663476572.....29340232714.....1239784258612

.0.0..1612568...146131060...10998070526....763669110112....50762954675186

.0.0.10566034..1503637694..178432948526..19447316121332..2032908127837419

.0.0.68136376.15223224224.2848000336302.487171820681716.80080573259154704

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1)

k=3: [order 14] for n>17

k=4: [order 46] for n>49

Example

Some solutions for n=4 k=4
..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..1..1..1. .0..0..1..1
..1..1..1..0. .1..0..0..0. .1..0..1..1. .1..0..1..0. .0..1..1..1
..1..0..0..1. .0..0..1..0. .1..0..1..0. .1..0..0..0. .1..1..0..1
..1..0..0..0. .1..1..0..0. .0..1..1..1. .0..1..0..1. .0..1..0..0

Crossrefs

Sequence in context: A279798 A191941 A087536 * A282338 A198210 A329061

Adjacent sequences: A281885 A281886 A281887 * A281889 A281890 A281891

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 01 2017

Status

approved