A300646 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 2, 4, 0, 0, 9, 10, 10, 9, 0, 0, 19, 30, 64, 30, 19, 0, 0, 41, 104, 316, 316, 104, 41, 0, 0, 88, 340, 1789, 2998, 1789, 340, 88, 0, 0, 189, 1144, 9738, 28089, 28089, 9738, 1144, 189, 0, 0, 406, 3795, 54293, 268615, 456649, 268615, 54293, 3795

Offset

1,8

Comments

Table starts

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

.0...1....2......4........9.........19...........41.............88

.0...2....2.....10.......30........104..........340...........1144

.0...4...10.....64......316.......1789.........9738..........54293

.0...9...30....316.....2998......28089.......268615........2552014

.0..19..104...1789....28089.....456649......7455411......121708555

.0..41..340...9738...268615....7455411....209156119.....5850560104

.0..88.1144..54293..2552014..121708555...5850560104...280782187131

.0.189.3795.300456.24338903.1990954802.164070075524.13506744672543

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)

k=3: [order 15]

k=4: [order 49]

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..1
..0..1..0..0. .0..1..0..0. .1..1..1..1. .1..1..0..0. .0..0..1..0
..1..1..0..0. .0..0..0..1. .1..0..1..1. .0..0..1..1. .1..1..0..0
..1..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..1..1. .1..0..0..0

Crossrefs

Column 2 is A078039(n-2).

Sequence in context: A317643 A179011 A300465 * A300776 A301400 A134315

Adjacent sequences: A300643 A300644 A300645 * A300647 A300648 A300649

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 10 2018

Status

approved