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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)