A305776 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 81, 65, 16, 32, 192, 292, 292, 192, 32, 64, 569, 1096, 1481, 1096, 569, 64, 128, 1709, 4172, 7528, 7528, 4172, 1709, 128, 256, 5162, 15953, 38623, 51586, 38623, 15953, 5162, 256, 512, 15663, 61111, 199257, 362200, 362200

Offset

1,2

Comments

Table starts

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

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

...4....23.....81.....292......1096.......4172.......15953.........61111

...8....65....292....1481......7528......38623......199257.......1028731

..16...192...1096....7528.....51586.....362200.....2553685......18030904

..32...569...4172...38623....362200....3492739....33891076.....329477646

..64..1709..15953..199257...2553685...33891076...453853629....6095547869

.128..5162..61111.1028731..18030904..329477646..6095547869..113299205109

.256.15663.234288.5312551.127390570.3206311981.81987206051.2110390711467

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..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..1
..1..1..0..0. .1..1..1..1. .1..1..1..0. .1..1..0..0. .1..0..1..1
..1..0..1..1. .0..0..1..0. .1..0..0..0. .1..1..1..0. .0..1..0..1
..1..1..1..1. .1..0..0..0. .0..0..1..0. .1..1..1..1. .0..1..0..0
..1..0..1..0. .0..0..0..1. .1..0..0..1. .0..1..1..0. .0..1..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A317230 A304310 A316209 * A317125 A305593 A317011

Adjacent sequences: A305773 A305774 A305775 * A305777 A305778 A305779

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 10 2018

Status

approved