A299514 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 29, 29, 23, 5, 8, 49, 63, 112, 63, 49, 8, 13, 99, 167, 439, 439, 167, 99, 13, 21, 189, 477, 1950, 2336, 1950, 477, 189, 21, 34, 383, 1233, 7702, 13836, 13836, 7702, 1233, 383, 34, 55, 777, 3265, 30277, 84449, 122197

Offset

1,5

Comments

Table starts

..0...1....1......2.......3........5..........8..........13............21

..1...3....7.....13......23.......49.........99.........189...........383

..1...7...15.....29......63......167........477........1233..........3265

..2..13...29....112.....439.....1950.......7702.......30277........126429

..3..23...63....439....2336....13836......84449......477162.......2791607

..5..49..167...1950...13836...122197....1190886....10305454......92938855

..8..99..477...7702...84449..1190886...17345466...225351737....3159884395

.13.189.1233..30277..477162.10305454..225351737..4446967161...94825218644

.21.383.3265.126429.2791607.92938855.3159884395.94825218644.3109567007082

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 15] for n>17

k=4: [order 68] for n>70

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A298582 A299574 A298396 * A299314 A300115 A100888

Adjacent sequences: A299511 A299512 A299513 * A299515 A299516 A299517

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 11 2018

Status

approved