A304427 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 124, 98, 3, 5, 383, 836, 836, 383, 5, 8, 1493, 5227, 9304, 5227, 1493, 8, 13, 5824, 33263, 98190, 98190, 33263, 5824, 13, 21, 22717, 210954, 1043316, 1712347, 1043316, 210954, 22717, 21, 34, 88609, 1338995

Offset

1,5

Comments

Table starts

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

..1.....7......25.........98..........383...........1493.............5824

..1....25.....124........836.........5227..........33263...........210954

..2....98.....836.......9304........98190........1043316.........11085965

..3...383....5227......98190......1712347.......30362267........536823135

..5..1493...33263....1043316.....30362267......898146670......26510744474

..8..5824..210954...11085965....536823135....26510744474....1305482386171

.13.22717.1338995..117776344...9501018264...783174010085...64363459841666

.21.88609.8497693.1251440091.168137854364.23137703330738.3173399640697899

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) +3*a(n-2) +2*a(n-3)

k=3: [order 9] for n>10

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

k=5: [order 90] for n>93

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A316383 A306143 A317376 * A316282 A305961 A317222

Adjacent sequences: A304424 A304425 A304426 * A304428 A304429 A304430

Keyword

nonn,tabl

Author

R. H. Hardin, May 12 2018

Status

approved