A317125 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 82, 65, 16, 32, 192, 302, 302, 192, 32, 64, 569, 1164, 1597, 1164, 569, 64, 128, 1709, 4561, 8598, 8598, 4561, 1709, 128, 256, 5162, 17966, 46955, 65099, 46955, 17966, 5162, 256, 512, 15663, 70913, 258241, 507378, 507378

Offset

1,2

Comments

Table starts

...1.....2......4.......8........16.........32...........64............128

...2.....8.....23......65.......192........569.........1709...........5162

...4....23.....82.....302......1164.......4561........17966..........70913

...8....65....302....1597......8598......46955.......258241........1422755

..16...192...1164....8598.....65099.....507378......3982123.......31333222

..32...569...4561...46955....507378....5694906.....64566869......734571604

..64..1709..17966..258241...3982123...64566869...1062867065....17593640188

.128..5162..70913.1422755..31333222..734571604..17593640188...424977120539

.256.15663.280153.7843425.246848528.8373046468.292154717629.10317078557668

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5

k=3: [order 16]

k=4: [order 57] for n>59

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A304310 A316209 A305776 * A305593 A317011 A316876

Adjacent sequences: A317122 A317123 A317124 * A317126 A317127 A317128

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 21 2018

Status

approved