A316239 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 57, 29, 29, 57, 13, 21, 125, 71, 105, 71, 125, 21, 34, 289, 153, 365, 365, 153, 289, 34, 55, 741, 358, 1135, 1867, 1135, 358, 741, 55, 89, 1737, 956, 4802, 6518, 6518, 4802, 956, 1737, 89, 144, 4045, 2612, 21363, 41303

Offset

1,2

Comments

Table starts

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

..2....5....9....21......57......125........289..........741..........1737

..3....9...14....29......71......153........358..........956..........2612

..5...21...29...105.....365.....1135.......4802........21363.........89321

..8...57...71...365....1867.....6518......41303.......312366.......1912290

.13..125..153..1135....6518....42075.....496125......5256306......54317972

.21..289..358..4802...41303...496125...10057887....174856739....2842217588

.34..741..956.21363..312366..5256306..174856739...5109468434..127247367597

.55.1737.2612.89321.1912290.54317972.2842217588.127247367597.4994868880193

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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)

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

k=4: [order 64] for n>67

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A316615 A316427 A317429 * A317160 A317043 A317697

Adjacent sequences: A316236 A316237 A316238 * A316240 A316241 A316242

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 27 2018

Status

approved