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A299194 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 3, 13, 8, 13, 34, 9, 9, 34, 13, 21, 73, 19, 80, 19, 73, 21, 34, 203, 59, 220, 220, 59, 203, 34, 55, 594, 129, 518, 1539, 518, 129, 594, 55, 89, 1443, 355, 2466, 3704, 3704, 2466, 355, 1443, 89, 144, 4013, 891, 8609, 25097, 11459, 25097 (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

..2....4...3....13.....34......73......203.......594.......1443.........4013

..3....3...3.....9.....19......59......129.......355........891.........2317

..5...13...9....80....220.....518.....2466......8609......26954.......108253

..8...34..19...220...1539....3704....25097....161188.....638942......3784977

.13...73..59...518...3704...11459....80188....533274....2432710.....15899938

.21..203.129..2466..25097...80188...848789...8080772...44495267....401953734

.34..594.355..8609.161188..533274..8080772.122310309..832353461..10703053961

.55.1443.891.26954.638942.2432710.44495267.832353461.6602925250.104043829095

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 17] for n>18

k=4: [order 69] for n>70

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A297901.

Sequence in context: A298501 A298320 A299393 * A300030 A232451 A299451

Adjacent sequences:  A299191 A299192 A299193 * A299195 A299196 A299197

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 04 2018

STATUS

approved

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Last modified August 12 09:17 EDT 2020. Contains 336438 sequences. (Running on oeis4.)