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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 A199512

Adjacent sequences:  A317263 A317264 A317265 * A317267 A317268 A317269

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 25 2018

STATUS

approved

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Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)