A317160 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 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, 29, 29, 57, 13, 21, 125, 73, 105, 73, 125, 21, 34, 289, 165, 379, 379, 165, 289, 34, 55, 741, 394, 1245, 2345, 1245, 394, 741, 55, 89, 1737, 1068, 5458, 9686, 9686, 5458, 1068, 1737, 89, 144, 4045, 3018, 25315, 65283

Offset

1,2

Comments

Table starts

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

..2....5....9.....21......57.......125........289..........741...........1737

..3....9...14.....29......73.......165........394.........1068...........3018

..5...21...29....105.....379......1245.......5458........25315.........111407

..8...57...73....379....2345......9686......65283.......549872........3771839

.13..125..165...1245....9686.....69701.....887617.....10940249......123485236

.21..289..394...5458...65283....887617...20168266....403588059.....7455221517

.34..741.1068..25315..549872..10940249..403588059..13792577708...402260884943

.55.1737.3018.111407.3771839.123485236.7455221517.402260884943.18922956181705

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 18] for n>20

k=4: [order 66] for n>69

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A316427 A317429 A316239 * A317043 A317697 A132403

Adjacent sequences: A317157 A317158 A317159 * A317161 A317162 A317163

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 22 2018

Status

approved