A317376 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 91, 86, 3, 5, 313, 529, 529, 313, 5, 8, 1145, 2870, 4811, 2870, 1145, 8, 13, 4184, 15382, 42512, 42512, 15382, 4184, 13, 21, 15293, 83982, 360940, 659721, 360940, 83982, 15293, 21, 34, 55895, 455180, 3113246, 9218534

Offset

1,5

Comments

Table starts

..0.....1.......1.........2...........3.............5...............8

..1.....7......23........86.........313..........1145............4184

..1....23......91.......529........2870.........15382...........83982

..2....86.....529......4811.......42512........360940.........3113246

..3...313....2870.....42512......659721.......9218534.......134524463

..5..1145...15382....360940.....9218534.....205048072......4822465183

..8..4184...83982...3113246...134524463....4822465183....185409601420

.13.15293..455180..26916032..1959207396..113269475813...7139196864817

.21.55895.2470224.231704568.28331771091.2632551285887.270802813530242

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) +a(n-2)

k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)

k=3: [order 15] for n>16

k=4: [order 50] for n>51

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A304597 A316383 A306143 * A304427 A316282 A305961

Adjacent sequences: A317373 A317374 A317375 * A317377 A317378 A317379

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 26 2018

Status

approved