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A299612 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 5
0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 179, 173, 63, 177, 21, 34, 359, 96, 322, 453, 453, 322, 96, 359, 34, 55, 705, 147, 635, 1006, 1223, 1006, 635, 147, 705, 55, 89, 1351 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0...1...1....2....3.....5......8......13......21.......34........55

..1...3...7...13...23....49.....95.....177.....359......705......1351

..1...7..15...19...23....34.....63......96.....147......233.......368

..2..13..19...40...85...173....322.....635....1325.....2806......5877

..3..23..23...85..179...453...1006....2523....6002....14802.....36299

..5..49..34..173..453..1223...3286....9873...28227....86428....253623

..8..95..63..322.1006..3286..13490...49047..183585...713699...2714170

.13.177..96..635.2523..9873..49047..231838.1084038..5339757..25938953

.21.359.147.1325.6002.28227.183585.1084038.6506278.41165944.255972254

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

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

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

k=4: [order 72] for n>73

EXAMPLE

Some solutions for n=6 k=6

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A298050.

Column 4 is A298656.

Sequence in context: A298055 A298888 A298660 * A297959 A298775 A298582

Adjacent sequences:  A299609 A299610 A299611 * A299613 A299614 A299615

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 14 2018

STATUS

approved

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Last modified May 28 15:04 EDT 2022. Contains 354115 sequences. (Running on oeis4.)