A299554 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 9, 6, 0, 0, 17, 31, 31, 17, 0, 0, 41, 166, 220, 166, 41, 0, 0, 104, 752, 2034, 2034, 752, 104, 0, 0, 261, 3739, 17565, 37283, 17565, 3739, 261, 0, 0, 655, 18300, 160089, 621694, 621694, 160089, 18300, 655, 0, 0, 1646, 90313, 1456436

Offset

1,8

Comments

Table starts

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

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

.0...3.....9.......31........166..........752............3739.............18300

.0...6....31......220.......2034........17565..........160089...........1456436

.0..17...166.....2034......37283.......621694........10759709.........186196755

.0..41...752....17565.....621694.....19604624.......648002718.......21337630973

.0.104..3739...160089...10759709....648002718.....40708113490.....2548695927399

.0.261.18300..1456436..186196755..21337630973...2548695927399...303433045764806

.0.655.90313.13302816.3228302388.704140369456.159913303887571.36196880526512847

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 37] for n>38

Example

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

Crossrefs

Column 2 is A297972.

Sequence in context: A268759 A298841 A299602 * A300175 A129533 A360849

Adjacent sequences: A299551 A299552 A299553 * A299555 A299556 A299557

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 12 2018

Status

approved