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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 09:53 EDT 2021. Contains 347612 sequences. (Running on oeis4.)