A283203 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors, with the exception of exactly one element.

0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 36, 83, 36, 0, 0, 176, 868, 868, 176, 0, 0, 824, 7899, 16048, 7899, 824, 0, 0, 3668, 66412, 263232, 263232, 66412, 3668, 0, 0, 15808, 535025, 4024168, 7842272, 4024168, 535025, 15808, 0, 0, 66640, 4184880, 59065412

Offset

1,8

Comments

Table starts

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

.0.....0........6..........36...........176..............824...............3668

.0.....6.......83.........868..........7899............66412.............535025

.0....36......868.......16048........263232..........4024168...........59065412

.0...176.....7899......263232.......7842272........218628378.........5855079969

.0...824....66412.....4024168.....218628378......11127848480.......544338609740

.0..3668...535025....59065412....5855079969.....544338609740.....48652102368973

.0.15808..4184880...842673912..152494818512...25902857395584...4230873205192882

.0.66640.32026556.11773250320.3891003515011.1207783406994400.360562132072479325

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 18]

k=4: [order 34]

k=5: [order 96]

Example

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

Crossrefs

Sequence in context: A281080 A283347 A334710 * A155742 A364406 A005597

Adjacent sequences: A283200 A283201 A283202 * A283204 A283205 A283206

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 02 2017

Status

approved