A304347 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 27, 28, 16, 32, 94, 71, 71, 94, 32, 64, 284, 225, 290, 225, 284, 64, 128, 752, 613, 1266, 1266, 613, 752, 128, 256, 2244, 1752, 4733, 6373, 4733, 1752, 2244, 256, 512, 6532, 5102, 18855, 27505, 27505, 18855, 5102, 6532, 512

Offset

1,2

Comments

Table starts

...1....2.....4......8......16.......32........64........128.........256

...2....4....14.....28......94......284.......752.......2244........6532

...4...14....27.....71.....225......613......1752.......5102.......14673

...8...28....71....290....1266.....4733.....18855......76887......308978

..16...94...225...1266....6373....27505....127511.....633229.....3052998

..32..284...613...4733...27505...135445....741942....4355191....24554331

..64..752..1752..18855..127511...741942...4921043...36193582...250785575

.128.2244..5102..76887..633229..4355191..36193582..343449680..2937754820

.256.6532.14673.308978.3052998.24554331.250785575.2937754820.30008468246

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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 57] for n>60

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A317238 A260038 A193916 * A316218 A305642 A317036

Adjacent sequences: A304344 A304345 A304346 * A304348 A304349 A304350

Keyword

nonn,tabl

Author

R. H. Hardin, May 11 2018

Status

approved