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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A003229(n-1).

Sequence in context: A341607 A303719 A299595 * A318545 A071450 A175457

Adjacent sequences: A304267 A304268 A304269 * A304271 A304272 A304273

Keyword

nonn,tabl

Author

R. H. Hardin, May 09 2018

Status

approved