A299334 T(n,k) = Number of n X k 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 7 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, 36, 36, 17, 0, 0, 41, 173, 263, 173, 41, 0, 0, 104, 858, 2537, 2537, 858, 104, 0, 0, 261, 4258, 22718, 46286, 22718, 4258, 261, 0, 0, 655, 21386, 214683, 816886, 816886, 214683, 21386, 655, 0, 0, 1646, 107465, 2024559

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......36.......173.........858..........4258...........21386

.0...6....36.....263......2537.......22718........214683.........2024559

.0..17...173....2537.....46286......816886......14783424.......267652693

.0..41...858...22718....816886....27685946.....967671172.....33782479865

.0.104..4258..214683..14783424...967671172...65181402152...4383565657986

.0.261.21386.2024559.267652693.33782479865.4383565657986.567774280392040

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 12] for n > 14;

k=4: [order 27] for n > 28;

k=5: [order 76] for n > 79.

Example

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

Crossrefs

Column 2 is A297972.

Sequence in context: A297978 A298629 A298461 * A268759 A298841 A299602

Adjacent sequences: A299331 A299332 A299333 * A299335 A299336 A299337

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 07 2018

Status

approved