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.

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

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

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..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

Adjacent sequences: A300027 A300028 A300029 * A300031 A300032 A300033

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 23 2018

Status

approved