A304302 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 3, 1, 3, 5, 8, 5, 5, 8, 5, 8, 5, 6, 4, 6, 5, 8, 13, 22, 14, 13, 13, 14, 22, 13, 21, 29, 22, 30, 62, 30, 22, 29, 21, 34, 60, 33, 43, 88, 88, 43, 33, 60, 34, 55, 121, 57, 129, 339, 237, 339, 129, 57, 121, 55, 89, 194, 97, 245, 888, 685, 685, 888, 245

Offset

1,5

Comments

Table starts

..0..1..1...2....3....5.....8.....13.....21......34.......55.......89.......144

..1..3..2...1....8....5....22.....29.....60.....121......194......425.......704

..1..2..3...5....6...14....22.....33.....57......97......159......255.......432

..2..1..5...4...13...30....43....129....245.....519.....1254.....2525......5707

..3..8..6..13...62...88...339....888...2108....6329....16064....43396....117393

..5..5.14..30...88..237...685...1827...4974...14425....38170...106811....300976

..8.22.22..43..339..685..2673..11690..31390..133744...470762..1540068...6102146

.13.29.33.129..888.1827.11690..47501.161251..821454..3119449.12780462..56341952

.21.60.57.245.2108.4974.31390.161251.555463.3235101.14367171.61271388.319305797

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-2) +3*a(n-3) +2*a(n-4) -4*a(n-6) -2*a(n-7) -a(n-8) -2*a(n-9)

k=4: [order 15] for n>19

k=5: [order 32] for n>34

k=6: [order 64] for n>66

Example

Some solutions for n=5 k=4
..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0
..1..0..0..0. .1..0..0..1. .0..0..0..1. .1..0..0..0. .1..0..0..1
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0
..1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..1..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297809 for n>2.

Sequence in context: A038575 A347430 A346491 * A305516 A305182 A291047

Adjacent sequences: A304299 A304300 A304301 * A304303 A304304 A304305

Keyword

nonn,tabl

Author

R. H. Hardin, May 10 2018

Status

approved