A299753 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 95, 88, 16, 32, 298, 375, 375, 298, 32, 64, 1012, 1524, 1998, 1524, 1012, 64, 128, 3440, 6170, 11733, 11733, 6170, 3440, 128, 256, 11700, 24838, 64703, 115279, 64703, 24838, 11700, 256, 512, 39804, 100272, 358219, 915181

Offset

1,2

Comments

Table starts

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

...2.....8.....26.......88.......298........1012.........3440..........11700

...4....26.....95......375......1524........6170........24838.........100272

...8....88....375.....1998.....11733.......64703.......358219........2010841

..16...298...1524....11733....115279......915181......7443583.......65049552

..32..1012...6170....64703....915181.....9822603....109073249.....1317338135

..64..3440..24838...358219...7443583...109073249...1686794332....28696396155

.128.11700.100272..2010841..65049552..1317338135..28696396155...723176599097

.256.39804.405068.11248655.548247606.15245980679.463029637815.16724897634952

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) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)

k=3: [order 18] for n>19

k=4: [order 65] for n>66

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A299852 A299008 A299675 * A300267 A318016 A320402

Adjacent sequences: A299750 A299751 A299752 * A299754 A299755 A299756

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 18 2018

Status

approved