A317043 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 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, 57, 33, 33, 57, 13, 21, 125, 90, 141, 90, 125, 21, 34, 289, 204, 610, 610, 204, 289, 34, 55, 741, 527, 2516, 6188, 2516, 527, 741, 55, 89, 1737, 1547, 14294, 35318, 35318, 14294, 1547, 1737, 89, 144, 4045, 4509, 88030

Offset

1,2

Comments

Table starts

..1....2....3......5........8.........13...........21.............34

..2....5....9.....21.......57........125..........289............741

..3....9...14.....33.......90........204..........527...........1547

..5...21...33....141......610.......2516........14294..........88030

..8...57...90....610.....6188......35318.......333207........4194626

.13..125..204...2516....35318.....393048......7760044......159647483

.21..289..527..14294...333207....7760044....302924053....11244564485

.34..741.1547..88030..4194626..159647483..11244564485...789775871803

.55.1737.4509.509381.41147020.2883656719.374107033198.46866337730606

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

k=3: [order 17] for n>19

k=4: [order 52] for n>55

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A317429 A316239 A317160 * A317697 A132403 A209167

Adjacent sequences: A317040 A317041 A317042 * A317044 A317045 A317046

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 19 2018

Status

approved