A299886 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 10, 16, 8, 13, 50, 28, 28, 50, 13, 21, 112, 44, 247, 44, 112, 21, 34, 348, 222, 677, 677, 222, 348, 34, 55, 1028, 573, 3597, 3127, 3597, 573, 1028, 55, 89, 2796, 1551, 21500, 16277, 16277, 21500, 1551, 2796, 89, 144, 8216, 5437, 101350

Offset

1,2

Comments

Table starts

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

..2....4....4.....16......50.......112.........348.........1028...........2796

..3....4...10.....28......44.......222.........573.........1551...........5437

..5...16...28....247.....677......3597.......21500.......101350.........547390

..8...50...44....677....3127.....16277......154308......1009789........7044041

.13..112..222...3597...16277....223094.....2596017.....24865898......323299576

.21..348..573..21500..154308...2596017....56762816....870847276....16820882455

.34.1028.1551.101350.1009789..24865898...870847276..20496493815...621532095596

.55.2796.5437.547390.7044041.323299576.16820882455.621532095596.32439092859262

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) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 18] for n>19

k=4: [order 66] for n>68

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A298230 A298154 A299128 * A299052 A299814 A299689

Adjacent sequences: A299883 A299884 A299885 * A299887 A299888 A299889

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 21 2018

Status

approved