A304270 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 6, 5, 8, 13, 7, 10, 10, 7, 13, 21, 13, 19, 21, 19, 13, 21, 34, 23, 37, 50, 50, 37, 23, 34, 55, 37, 67, 116, 146, 116, 67, 37, 55, 89, 63, 124, 259, 404, 404, 259, 124, 63, 89, 144, 109, 235, 601, 1074, 1246, 1074, 601, 235, 109, 144, 233

Offset: 1

Author

R. H. Hardin, May 09 2018

Keywords

• nonn
• tabl

Comments

Table starts

..1..2...3....5....8....13.....21......34......55.......89.......144.......233

..2..1...3....5....7....13.....23......37......63......109.......183.......309

..3..3...6...10...19....37.....67.....124.....235......436.......808......1513

..5..5..10...21...50...116....259.....601....1397.....3196......7359.....17016

..8..7..19...50..146...404...1074....2990....8316....22660.....62314....172244

.13.13..37..116..404..1246...3788...12342...39252...122156....388150...1234248

.21.23..67..259.1074..3788..13767...53839..201274...741275...2806825..10575217

.34.37.124..601.2990.12342..53839..252509.1118021..4901568..22174589..99427544

.55.63.235.1397.8316.39252.201274.1118021.5755625.29475545.156881417.822798993

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1012

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A003229(n-1).

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +3*a(n-3) for n>4

k=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +a(n-4) -3*a(n-5) -3*a(n-6) for n>7

k=5: [order 9] for n>10

k=6: [order 12] for n>13

k=7: [order 24] for n>25