A316176 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 16, 10, 3, 5, 51, 34, 34, 51, 5, 8, 165, 113, 72, 113, 165, 8, 13, 306, 275, 331, 331, 275, 306, 13, 21, 993, 604, 1425, 3087, 1425, 604, 993, 21, 34, 2867, 1804, 5297, 16382, 16382, 5297, 1804, 2867, 34, 55, 6818, 4683, 18573, 66575

Offset

1,5

Comments

Table starts

..0....1....1.....2.......3.........5..........8...........13............21

..1....3...11....10......51.......165........306..........993..........2867

..1...11...16....34.....113.......275........604.........1804..........4683

..2...10...34....72.....331......1425.......5297........18573.........84658

..3...51..113...331....3087.....16382......66575.......500251.......3416740

..5..165..275..1425...16382....139293.....976178.....10070845.....106916450

..8..306..604..5297...66575....976178...12236682....164577403....2930093529

.13..993.1804.18573..500251..10070845..164577403...4139589568..113829450853

.21.2867.4683.84658.3416740.106916450.2930093529.113829450853.4957413596069

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 18] for n>20

k=4: [order 64] for n>66

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A316455 A305015 A316648 * A317458 A301615 A180771

Adjacent sequences: A316173 A316174 A316175 * A316177 A316178 A316179

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 25 2018

Status

approved