A305593 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 95, 65, 16, 32, 192, 390, 390, 192, 32, 64, 569, 1626, 2451, 1626, 569, 64, 128, 1709, 6818, 14746, 14746, 6818, 1709, 128, 256, 5162, 28530, 89466, 126484, 89466, 28530, 5162, 256, 512, 15663, 119266, 544280, 1103744

Offset

1,2

Comments

Table starts

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

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

...4....23.....95......390......1626........6818.........28530.........119266

...8....65....390.....2451.....14746.......89466........544280........3314595

..16...192...1626....14746....126484.....1103744.......9637513.......84163172

..32...569...6818....89466...1103744....13941521.....175683720.....2213918787

..64..1709..28530...544280...9637513...175683720....3190446497....57940960729

.128..5162.119266..3314595..84163172..2213918787...57940960729..1517186100046

.256.15663.498890.20186517.735136189.27910555993.1053163229940.39781453968523

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 57] for n>59

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A316209 A305776 A317125 * A317011 A316876 A317604

Adjacent sequences: A305590 A305591 A305592 * A305594 A305595 A305596

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 05 2018

Status

approved