A297978 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 8, 6, 0, 0, 17, 20, 20, 17, 0, 0, 41, 124, 109, 124, 41, 0, 0, 104, 501, 1042, 1042, 501, 104, 0, 0, 261, 2410, 7302, 18037, 7302, 2410, 261, 0, 0, 655, 11304, 60427, 242401, 242401, 60427, 11304, 655, 0, 0, 1646, 53108, 481401, 3565760

Offset

1,8

Comments

Table starts

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

.0...1.....3.......6........17...........41............104..............261

.0...3.....8......20.......124..........501...........2410............11304

.0...6....20.....109......1042.........7302..........60427...........481401

.0..17...124....1042.....18037.......242401........3565760.........52222182

.0..41...501....7302....242401......5902043......160132152.......4278426570

.0.104..2410...60427...3565760....160132152.....7833283900.....380347270776

.0.261.11304..481401..52222182...4278426570...380347270776...33544649054853

.0.655.53108.3880101.765460393.114579985316.18479502350618.2962364663254528

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

k=3: [order 13] for n>15

k=4: [order 46] for n>49

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..1..1
..0..1..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..0. .1..0..0..1
..0..0..1..1. .1..1..0..1. .0..0..1..1. .1..0..1..1. .1..1..1..0
..1..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..1..0. .0..0..1..0
..1..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

Crossrefs

Sequence in context: A152893 A335682 A335681 * A298629 A298461 A299334

Adjacent sequences: A297975 A297976 A297977 * A297979 A297980 A297981

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2018

Status

approved