A283494 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 12, 59, 12, 0, 0, 64, 576, 576, 64, 0, 0, 312, 5444, 10000, 5444, 312, 0, 0, 1460, 47712, 174232, 174232, 47712, 1460, 0, 0, 6624, 402588, 2836520, 5691512, 2836520, 402588, 6624, 0, 0, 29394, 3304736, 44556288

Offset

1,8

Comments

Table starts

.0.....0........0...........0.............0................0..................0

.0.....0........2..........12............64..............312...............1460

.0.....2.......59.........576..........5444............47712.............402588

.0....12......576.......10000........174232..........2836520...........44556288

.0....64.....5444......174232.......5691512........173139952.........5074155320

.0...312....47712.....2836520.....173139952.......9816981756.......536229705204

.0..1460...402588....44556288....5074155320.....536229705204.....54620836862500

.0..6624..3304736...682531252..145077026768...28589370541536...5432594465187864

.0.29394.26585976.10259419732.4069261870596.1495349029171972.530096184197639160

Links

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

Formula

Empirical for column k:

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

k=2: [order 10]

k=3: [order 10] for n>13

k=4: [order 26] for n>29

k=5: [order 74] for n>77

Example

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

Crossrefs

Sequence in context: A037224 A122670 A352661 * A353254 A281034 A282441

Adjacent sequences: A283491 A283492 A283493 * A283495 A283496 A283497

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 08 2017

Status

approved