A284075 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 15, 0, 0, 0, 33, 275, 314, 0, 0, 0, 176, 3174, 7302, 3764, 0, 0, 0, 858, 31898, 147864, 151310, 37557, 0, 0, 0, 4000, 300008, 2696970, 5555954, 2816826, 353608, 0, 0, 0, 18298, 2695374, 45973823, 189363893, 188451507

Offset

1,12

Comments

Table starts

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

.0.0......1........6.........33..........176............858.............4000

.0.0.....15......275.......3174........31898.........300008..........2695374

.0.0....314.....7302.....147864......2696970.......45973823........754541156

.0.0...3764...151310....5555954....189363893.....5950703039.....179626388248

.0.0..37557..2816826..188451507..11888242488...690497721277...38373427448124

.0.0.353608.48994058.6011835223.700044712076.74965549398304.7663959789277668

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 24]

k=4: [order 51]

Empirical for row n:

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

n=2: [order 12]

n=3: [order 42]

n=4: [order 84]

Example

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

Crossrefs

Sequence in context: A364530 A263695 A158965 * A281693 A013314 A328339

Adjacent sequences: A284072 A284073 A284074 * A284076 A284077 A284078

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 19 2017

Status

approved