A299393 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6 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, 17, 63, 17, 73, 21, 34, 203, 48, 119, 119, 48, 203, 34, 55, 594, 94, 243, 508, 243, 94, 594, 55, 89, 1443, 234, 1086, 934, 934, 1086, 234, 1443, 89, 144, 4013, 589, 2782, 6254, 2483, 6254, 2782, 589

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.....17.....48......94......234.......589.......1333

..5...13...9...63....119....243....1086.....2782......8509......31229

..8...34..17..119....508....934....6254....28963....110704.....623533

.13...73..48..243....934...2483...11240....48286....252027....1266960

.21..203..94.1086...6254..11240..112188...649720...3226442...27461474

.34..594.234.2782..28963..48286..649720..5884463..35846074..446459559

.55.1443.589.8509.110704.252027.3226442.35846074.286590596.3734068803

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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 71] for n>72

Example

Some solutions for n=5 k=7
..0..0..0..1..1..1..1. .0..0..0..0..1..1..1. .0..0..0..0..1..0..1
..1..1..0..0..0..1..1. .0..0..1..1..1..0..0. .0..0..1..1..1..1..0
..0..0..0..0..0..0..0. .1..1..1..1..1..1..1. .1..1..1..1..1..1..1
..1..1..0..0..0..1..1. .0..0..1..1..1..0..0. .0..0..1..1..1..1..0
..0..0..0..1..1..1..1. .0..0..0..0..1..1..1. .0..0..0..0..1..0..1

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A297901.

Column 3 is A298315.

Column 4 is A298316.

Sequence in context: A297907 A298501 A298320 * A299194 A300030 A232451

Adjacent sequences: A299390 A299391 A299392 * A299394 A299395 A299396

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 09 2018

Status

approved