A316925 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 31, 31, 57, 13, 21, 125, 81, 137, 81, 125, 21, 34, 289, 184, 594, 594, 184, 289, 34, 55, 741, 492, 2574, 6339, 2574, 492, 741, 55, 89, 1737, 1457, 15118, 40938, 40938, 15118, 1457, 1737, 89, 144, 4045, 4371, 95244

Offset

1,2

Comments

Table starts

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

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

..3....9...13.....31.......81........184..........492............1457

..5...21...31....137......594.......2574........15118...........95244

..8...57...81....594.....6339......40938.......428394.........5627600

.13..125..184...2574....40938.....533726.....11571636.......256609365

.21..289..492..15118...428394...11571636....493774680.....20147703090

.34..741.1457..95244..5627600..256609365..20147703090...1580858618327

.55.1737.4371.569635.59111561.5035506864.740128547549.105913781465166

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 51] for n>55

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A304355 A305918 A305649 * A305347 A316615 A316427

Adjacent sequences: A316922 A316923 A316924 * A316926 A316927 A316928

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 16 2018

Status

approved