A317697 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 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, 57, 33, 33, 57, 13, 21, 125, 92, 141, 92, 125, 21, 34, 289, 220, 630, 630, 220, 289, 34, 55, 741, 593, 2742, 6984, 2742, 593, 741, 55, 89, 1737, 1787, 16008, 45681, 45681, 16008, 1787, 1737, 89, 144, 4045, 5401, 100830

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.......92........220..........593............1787

..5...21...33....141......630.......2742........16008..........100830

..8...57...92....630.....6984......45681.......464357.........6124074

.13..125..220...2742....45681.....585418.....12414382.......278773058

.21..289..593..16008...464357...12414382....526480617.....21681685596

.34..741.1787.100830..6124074..278773058..21681685596...1721401739325

.55.1737.5401.603699.64822432.5491231349.800622189621.116191191089274

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..0..1. .0..1..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..1. .1..0..1..0
..1..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..1..0. .1..1..0..1
..0..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..1..0
..0..0..0..0. .0..0..0..0. .0..1..1..0. .1..0..1..1. .1..0..1..1

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A316239 A317160 A317043 * A132403 A209167 A299995

Adjacent sequences: A317694 A317695 A317696 * A317698 A317699 A317700

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 04 2018

Status

approved