A316876 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 99, 65, 16, 32, 192, 425, 425, 192, 32, 64, 569, 1877, 2931, 1877, 569, 64, 128, 1709, 8333, 19363, 19363, 8333, 1709, 128, 256, 5162, 36900, 129974, 191678, 129974, 36900, 5162, 256, 512, 15663, 163433, 871345, 1956634

Offset

1,2

Comments

Table starts

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

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

...4....23.....99......425.......1877.........8333.........36900

...8....65....425.....2931......19363.......129974........871345

..16...192...1877....19363.....191678......1956634......19933839

..32...569...8333...129974....1956634.....30894538.....486546897

..64..1709..36900...871345...19933839....486546897...11836970493

.128..5162.163433..5848852..202681853...7638934647..286716424150

.256.15663.724406.39278049.2064146570.120283055361.6977675255288

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] for n>17

k=4: [order 56] for n>58

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A317125 A305593 A317011 * A317604 A038208 A240484

Adjacent sequences: A316873 A316874 A316875 * A316877 A316878 A316879

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 15 2018

Status

approved