A303690 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 2, 18, 0, 0, 61, 20, 20, 61, 0, 0, 209, 27, 138, 27, 209, 0, 0, 702, 108, 343, 343, 108, 702, 0, 0, 2381, 191, 1744, 349, 1744, 191, 2381, 0, 0, 8069, 599, 5563, 2809, 2809, 5563, 599, 8069, 0, 0, 27330, 1261, 23963, 4619, 19068, 4619

Offset

1,5

Comments

Table starts

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

.0....3....5....18....61....209.....702.....2381.....8069.....27330......92581

.0....5....2....20....27....108.....191......599.....1261......3503.......8019

.0...18...20...138...343...1744....5563....23963....85439....343499....1279385

.0...61...27...343...349...2809....4619....29475....59695....312565.....749915

.0..209..108..1744..2809..19068...55382...273621...934066...4202604...15472710

.0..702..191..5563..4619..55382...99205...713542..1964803..10454428...36456925

.0.2381..599.23963.29475.273621..713542..5047477.16751184.100553061..399751263

.0.8069.1261.85439.59695.934066.1964803.16751184.58634971.399564046.1713589379

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

k=3: [order 16] for n>18

k=4: [order 31] for n>35

k=5: [order 93] for n>97

Example

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

Crossrefs

Sequence in context: A115013 A072736 A135090 * A304156 A305509 A305175

Adjacent sequences: A303687 A303688 A303689 * A303691 A303692 A303693

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 28 2018

Status

approved