A299015 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 44, 44, 73, 32, 64, 157, 123, 174, 123, 157, 64, 128, 353, 343, 1052, 1052, 343, 353, 128, 256, 869, 957, 4488, 6908, 4488, 957, 869, 256, 512, 1993, 2710, 18758, 39124, 39124, 18758, 2710, 1993, 512, 1024

Offset

1,2

Comments

Table starts

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

...2....7...13.....29.......73.......157.........353..........869

...4...13...20.....44......123.......343.........957.........2710

...8...29...44....174.....1052......4488.......18758........89713

..16...73..123...1052.....6908.....39124......259556......1718835

..32..157..343...4488....39124....379236.....3848010.....39235328

..64..353..957..18758...259556...3848010....59666756....931277377

.128..869.2710..89713..1718835..39235328...931277377..22388413097

.256.1993.7749.409166.11081989.404291236.14739630633.545009501463

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) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6.

k=3: [order 16] for n>17.

k=4: [order 66] for n>70.

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A299350 A299097 A299879 * A299806 A299682 A300314

Adjacent sequences: A299012 A299013 A299014 * A299016 A299017 A299018

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 31 2018

Status

approved