A299806 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 8 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, 1059, 1059, 343, 353, 128, 256, 869, 973, 4543, 7013, 4543, 973, 869, 256, 512, 1993, 2774, 19006, 40015, 40015, 19006, 2774, 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.........973.........2774

...8...29...44....174.....1059......4543.......19006........90935

..16...73..123...1059.....7013.....40015......265422......1763437

..32..157..343...4543....40015....388453.....3956148.....40566160

..64..353..973..19006...265422...3956148....61726046....969500658

.128..869.2774..90935..1763437..40566160...969500658..23457257837

.256.1993.7993.415860.11422152.419678087.15429018063.574690229422

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..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1
..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A299097 A299879 A299015 * A299682 A300314 A280604

Adjacent sequences: A299803 A299804 A299805 * A299807 A299808 A299809

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2018

Status

approved