A305347 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 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, 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, 1729, 1729, 1074, 505, 1205, 89, 144, 2681, 1037, 2619, 4685, 5408

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...1729...4685...13671....38115....105379....298557

.13..105..126..454..1729...5408..17054...58109...187782....603230...1995190

.21..237..245.1074..4685..17054..64658..259281...981360...3731097..14545752

.34..577..505.2619.13671..58109.259281.1241359..5567478..25026350.115911873

.55.1205.1037.6216.38115.187782.981360.5567478.29268593.154351497.843143816

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

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 37] for n>48

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303963.

Sequence in context: A305918 A305649 A316925 * A316615 A316427 A317429

Adjacent sequences: A305344 A305345 A305346 * A305348 A305349 A305350

Keyword

nonn,tabl

Author

R. H. Hardin, May 30 2018

Status

approved