login
A317004
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 162, 112, 16, 32, 420, 894, 894, 420, 32, 64, 1576, 4905, 7665, 4905, 1576, 64, 128, 5912, 26952, 65047, 65047, 26952, 5912, 128, 256, 22176, 148138, 551591, 854383, 551591, 148138, 22176, 256, 512, 83184, 814090
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4.........8..........16............32..............64
...2.....8......30.......112.........420..........1576............5912
...4....30.....162.......894........4905.........26952..........148138
...8...112.....894......7665.......65047........551591.........4691054
..16...420....4905.....65047......854383......11158663.......146589898
..32..1576...26952....551591....11158663.....223714229......4522081307
..64..5912..148138...4691054...146589898....4522081307....140997597309
.128.22176..814090..39872525..1924812465...91395911298...4396796733747
.256.83184.4474116.338839996.25259268302.1845641069555.136949793274310
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3)
k=3: [order 11] for n>12
k=4: [order 38] for n>39
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
..0..0..0..0. .0..1..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..1
..0..1..0..0. .1..1..1..0. .0..0..0..0. .1..1..1..0. .0..1..0..1
..0..1..1..0. .1..1..1..1. .1..0..0..0. .1..1..1..0. .1..1..1..0
..1..1..1..1. .0..0..1..1. .1..1..1..0. .1..0..0..1. .0..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A281949.
Sequence in context: A305769 A317118 A305530 * A316822 A317572 A281837
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 18 2018
STATUS
approved