A316130 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 60, 45, 3, 5, 120, 197, 197, 120, 5, 8, 333, 816, 1112, 816, 333, 8, 13, 928, 3421, 6562, 6562, 3421, 928, 13, 21, 2613, 13488, 36480, 58172, 36480, 13488, 2613, 21, 34, 7400, 54585, 204465, 493599, 493599, 204465, 54585

Offset

1,5

Comments

Table starts

..0....1......1.......2.........3...........5............8.............13

..1....7.....16......45.......120.........333..........928...........2613

..1...16.....60.....197.......816........3421........13488..........54585

..2...45....197....1112......6562.......36480.......204465........1170851

..3..120....816....6562.....58172......493599......4133986.......35123927

..5..333...3421...36480....493599.....6605359.....83789779.....1087380450

..8..928..13488..204465...4133986....83789779...1573249156....30313615055

.13.2613..54585.1170851..35123927..1087380450..30313615055...869530995479

.21.7400.222050.6622412.298723540.14339113742.599085201676.25944283079862

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) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 67] for n>69

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A316641 A304697 A316448 * A317436 A303896 A305288

Adjacent sequences: A316127 A316128 A316129 * A316131 A316132 A316133

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 24 2018

Status

approved