A316427 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 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, 53, 32, 32, 53, 13, 21, 105, 75, 97, 75, 105, 21, 34, 237, 148, 279, 279, 148, 237, 34, 55, 577, 311, 640, 1097, 640, 311, 577, 55, 89, 1205, 687, 1660, 2861, 2861, 1660, 687, 1205, 89, 144, 2681, 1443, 4353, 8761, 8916

Offset

1,2

Comments

Table starts

..1....2....3.....5.....8.....13......21.......34.......55........89........144

..2....5....9....21....53....105.....237......577.....1205......2681.......6349

..3....9...14....32....75....148.....311......687.....1443......3042.......6534

..5...21...32....97...279....640....1660.....4353....10975.....28038......72143

..8...53...75...279..1097...2861....8761....29548....87743....267014.....852011

.13..105..148...640..2861...8916...31433...121028...417457...1475614....5432803

.21..237..311..1660..8761..31433..130402...585212..2366785...9815061...42205654

.34..577..687..4353.29548.121028..585212..3242010.15459503..75494391..392102065

.55.1205.1443.10975.87743.417457.2366785.15459503.86620644.498441146.3054494072

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 42] for n>43

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303963.

Sequence in context: A316925 A305347 A316615 * A317429 A316239 A317160

Adjacent sequences: A316424 A316425 A316426 * A316428 A316429 A316430

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 02 2018

Status

approved