A317266 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 21, 21, 35, 13, 21, 61, 46, 74, 46, 61, 21, 34, 127, 91, 158, 158, 91, 127, 34, 55, 265, 186, 440, 718, 440, 186, 265, 55, 89, 507, 409, 1220, 1964, 1964, 1220, 409, 507, 89, 144, 1013, 892, 3655, 6645, 7477, 6645

Offset

1,2

Comments

Table starts

..1...2...3.....5......8.....13......21........34.........55..........89

..2...5...7....17.....35.....61.....127.......265........507........1013

..3...7..10....21.....46.....91.....186.......409........892........1931

..5..17..21....74....158....440....1220......3655......10907.......33353

..8..35..46...158....718...1964....6645.....27514.....103293......402198

.13..61..91...440...1964...7477...33695....166051.....806730.....4131259

.21.127.186..1220...6645..33695..219131...1493369....9934644....70625395

.34.265.409..3655..27514.166051.1493369..13595141..120265219..1153409542

.55.507.892.10907.103293.806730.9934644.120265219.1430955986.18455258095

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 16]

k=4: [order 67] for n>68

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A305252 A316552 A316311 * A067330 A202874 A355197

Adjacent sequences: A317263 A317264 A317265 * A317267 A317268 A317269

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 25 2018

Status

approved