A317011 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 96, 65, 16, 32, 192, 400, 400, 192, 32, 64, 569, 1704, 2567, 1704, 569, 64, 128, 1709, 7313, 16048, 16048, 7313, 1709, 128, 256, 5162, 31328, 101054, 147281, 101054, 31328, 5162, 256, 512, 15663, 134118, 639838, 1372782

Offset

1,2

Comments

Table starts

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

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

...4....23.....96......400.......1704........7313.........31328..........134118

...8....65....400.....2567......16048......101054........639838.........4056201

..16...192...1704....16048.....147281.....1372782......12838095.......120108770

..32...569...7313...101054....1372782....19006132.....263269309......3646120276

..64..1709..31328...639838...12838095...263269309....5395769696....110527120611

.128..5162.134118..4056201..120108770..3646120276..110527120611...3348077796513

.256.15663.574442.25720439.1124195594.50524538223.2265876477133.101540680029955

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A305776 A317125 A305593 * A316876 A317604 A038208

Adjacent sequences: A317008 A317009 A317010 * A317012 A317013 A317014

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 18 2018

Status

approved