A317153 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 36, 28, 16, 32, 94, 102, 102, 94, 32, 64, 284, 389, 416, 389, 284, 64, 128, 752, 1251, 2313, 2313, 1251, 752, 128, 256, 2244, 4091, 10682, 19580, 10682, 4091, 2244, 256, 512, 6532, 13931, 49746, 120427, 120427, 49746

Offset

1,2

Comments

Table starts

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

...2....4....14......28.......94.......284.........752.........2244

...4...14....36.....102......389......1251........4091........13931

...8...28...102.....416.....2313.....10682.......49746.......244887

..16...94...389....2313....19580....120427......786868......5565982

..32..284..1251...10682...120427....960577.....8398085.....79355311

..64..752..4091...49746...786868...8398085...100639070...1322153771

.128.2244.13931..244887..5565982..79355311..1322153771..24402104731

.256.6532.46536.1177228.37386216.704559110.16079639203.409040712216

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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>16

k=4: [order 69] for n>70

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A305642 A317036 A305911 * A316883 A317611 A220461

Adjacent sequences: A317150 A317151 A317152 * A317154 A317155 A317156

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 22 2018

Status

approved