A298320 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 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, 507, 243, 94, 594, 55, 89, 1443, 234, 1086, 934, 934, 1086, 234, 1443, 89, 144, 4013, 589, 2782, 6236, 2466, 6236, 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....507....934....6236....28894....110488.....622009

.13...73..48..243....934...2466...11175....48002....249672....1256472

.21..203..94.1086...6236..11175..111137...644056...3190955...27151266

.34..594.234.2782..28894..48002..644056..5833295..35487422..441894670

.55.1443.589.8509.110488.249672.3190955.35487422.281897638.3673383638

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=7, k=4
..0..1..0..1. .0..1..1..0. .0..0..1..1. .0..1..0..1. .0..1..1..0
..0..1..0..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .1..1..0..1
..1..1..1..1. .0..1..0..0. .1..0..1..0. .0..1..0..0. .0..1..0..0
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..1..1..0. .1..1..0..0. .0..0..1..1. .1..1..0..1. .0..0..0..1
..0..1..0..0. .1..1..1..0. .0..0..0..1. .0..1..0..0. .0..1..0..0
..1..0..0..1. .0..1..1..0. .1..0..0..1. .1..0..0..1. .1..0..0..0

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A297901.

Sequence in context: A187199 A297907 A298501 * A299393 A299194 A300030

Adjacent sequences: A298317 A298318 A298319 * A298321 A298322 A298323

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 17 2018

Status

approved