A316615 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 7 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, 28, 28, 53, 13, 21, 105, 63, 77, 63, 105, 21, 34, 237, 126, 199, 199, 126, 237, 34, 55, 577, 245, 454, 649, 454, 245, 577, 55, 89, 1205, 505, 1074, 1749, 1749, 1074, 505, 1205, 89, 144, 2681, 1037, 2619, 4719, 5464

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...28....63....126....245.....505.....1037......2088......4230

..5...21...28...77...199....454...1074....2619.....6216.....14782.....35494

..8...53...63..199...649...1749...4719...13770....38535....106694....302759

.13..105..126..454..1749...5464..17224...58861...190509....613009...2033562

.21..237..245.1074..4719..17224..65158..261426...990387...3768844..14720334

.34..577..505.2619.13770..58861.261426.1249304..5600646..25176200.116672242

.55.1205.1037.6216.38535.190509.990387.5600646.29420195.155127330.847493564

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

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 36] for n>37

k=5: [order 40] for n>51

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303963.

Column 3 is A305342.

Column 4 is A305343.

Sequence in context: A305649 A316925 A305347 * A316427 A317429 A316239

Adjacent sequences: A316612 A316613 A316614 * A316616 A316617 A316618

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 08 2018

Status

approved