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A298154 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero. 8
1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 6, 16, 8, 13, 50, 18, 18, 50, 13, 21, 112, 15, 196, 15, 112, 21, 34, 348, 104, 497, 497, 104, 348, 34, 55, 1028, 227, 2618, 1822, 2618, 227, 1028, 55, 89, 2796, 510, 15694, 7250, 7250, 15694, 510, 2796, 89, 144, 8216, 2020, 74848, 72678 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2....3......5.......8........13.........21...........34.............55

..2....4....4.....16......50.......112........348.........1028...........2796

..3....4....6.....18......15.......104........227..........510...........2020

..5...16...18....196.....497......2618......15694........74848.........398520

..8...50...15....497....1822......7250......72678.......448220........2829887

.13..112..104...2618....7250....111350....1177545.....10544116......137536697

.21..348..227..15694...72678...1177545...25625864....356815204.....6737133411

.34.1028..510..74848..448220..10544116..356815204...7382868491...216982050084

.55.2796.2020.398520.2829887.137536697.6737133411.216982050084.11381281119654

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 18] for n>19

k=4: [order 66] for n>68

EXAMPLE

Some solutions for n=6 k=4

..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..1

..1..1..0..1. .0..0..1..0. .1..0..1..1. .1..0..0..0. .1..1..0..0

..0..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0. .1..1..0..0

..1..1..0..1. .0..0..1..0. .0..0..0..1. .1..1..0..1. .1..1..0..1

..0..1..0..0. .1..1..1..1. .1..1..0..0. .1..0..0..0. .0..1..0..0

..0..1..0..0. .0..0..1..1. .1..1..0..0. .0..1..0..1. .1..0..0..0

CROSSREFS

Column 1 is A000045(n+1).

Sequence in context: A232451 A299451 A298230 * A299128 A299052 A299689

Adjacent sequences:  A298151 A298152 A298153 * A298155 A298156 A298158

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 13 2018

STATUS

approved

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Last modified February 19 02:06 EST 2018. Contains 299330 sequences. (Running on oeis4.)