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A300030 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 5
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, 1637, 518, 129, 594, 55, 89, 1443, 355, 2466, 4320, 4320, 2466, 355, 1443, 89, 144, 4013, 891, 8609, 30072, 18775, 30072 (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...3....13.....34......73.......203........594........1443
..3....3...3.....9.....19......59.......129........355.........891
..5...13...9....80....220.....518......2466.......8609.......26954
..8...34..19...220...1637....4320.....30072.....206967......903664
.13...73..59...518...4320...18775....153289....1162345.....7133776
.21..203.129..2466..30072..153289...1841903...19059670...151628931
.34..594.355..8609.206967.1162345..19059670..326461365..3425833703
.55.1443.891.26954.903664.7133776.151628931.3425833703.50773963070
LINKS
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..0. .0..0..1..0. .0..1..0..0. .0..1..1..0. .0..1..0..1
..0..0..0..1. .0..0..1..0. .1..0..0..0. .1..1..1..0. .0..1..0..1
..1..0..0..0. .1..0..1..1. .1..1..1..1. .0..1..1..1. .1..1..1..1
..0..0..0..1. .0..0..1..1. .0..1..0..0. .1..1..1..1. .0..1..0..1
..0..0..1..0. .1..0..0..0. .0..1..0..0. .1..1..0..0. .0..1..0..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A297901.
Column 3 is A299189.
Column 4 is A299190.
Sequence in context: A298320 A299393 A299194 * A232451 A299451 A300089
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 23 2018
STATUS
approved

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Last modified February 25 04:28 EST 2024. Contains 370309 sequences. (Running on oeis4.)