A300465 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 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, 8, 8, 9, 0, 0, 19, 22, 28, 22, 19, 0, 0, 41, 68, 142, 142, 68, 41, 0, 0, 88, 212, 540, 1146, 540, 212, 88, 0, 0, 189, 652, 2585, 7456, 7456, 2585, 652, 189, 0, 0, 406, 2017, 11343, 55663, 78195, 55663, 11343, 2017, 406, 0, 0

Offset

1,8

Comments

Table starts

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

.0...1....2.....4.......9........19.........41...........88............189

.0...2....2.....8......22........68........212..........652...........2017

.0...4....8....28.....142.......540.......2585........11343..........51501

.0...9...22...142....1146......7456......55663.......400028........2906875

.0..19...68...540....7456.....78195.....935121.....10913850......127028268

.0..41..212..2585...55663....935121...17675111....330639367.....6123205255

.0..88..652.11343..400028..10913850..330639367...9829599051...293961266876

.0.189.2017.51501.2906875.127028268.6123205255.293961266876.14061129641181

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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 52] for n>54

Example

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

Crossrefs

Column 2 is A078039(n-2).

Sequence in context: A138270 A317643 A179011 * A300646 A300776 A301400

Adjacent sequences: A300462 A300463 A300464 * A300466 A300467 A300468

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 06 2018

Status

approved