A317429 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 53, 32, 32, 53, 13, 21, 105, 75, 97, 75, 105, 21, 34, 237, 148, 279, 279, 148, 237, 34, 55, 577, 311, 640, 1097, 640, 311, 577, 55, 89, 1205, 687, 1666, 2891, 2891, 1666, 687, 1205, 89, 144, 2681, 1443, 4365, 8887, 9116

Offset

1,2

Comments

Table starts

..1....2....3.....5.....8.....13......21.......34.......55........89........144

..2....5....9....21....53....105.....237......577.....1205......2681.......6349

..3....9...14....32....75....148.....311......687.....1443......3042.......6534

..5...21...32....97...279....640....1666.....4365....11025.....28226......72631

..8...53...75...279..1097...2891....8887....30029....89848....274792.....882160

.13..105..148...640..2891...9116...32359...125832...439409...1569243....5838001

.21..237..311..1666..8887..32359..135880...617692..2534229..10679366...46580215

.34..577..687..4365.30029.125832..617692..3452903.16763615..83384489..439271584

.55.1205.1443.11025.89848.439409.2534229.16763615.95798175.562775876.3505340437

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: [order 12]

k=4: [order 40] for n>41

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303963.

Column 3 is A316422.

Sequence in context: A305347 A316615 A316427 * A316239 A317160 A317043

Adjacent sequences: A317426 A317427 A317428 * A317430 A317431 A317432

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 27 2018

Status

approved