A298396 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 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, 432, 432, 167, 99, 13, 21, 189, 473, 1915, 2231, 1915, 473, 189, 21, 34, 383, 1205, 7556, 13271, 13271, 7556, 1205, 383, 34, 55, 777, 3161, 29657, 81019, 117184

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........473........1205..........3161

..2..13...29....112.....432.....1915.......7556.......29657........123601

..3..23...63....432....2231....13271......81019......454822.......2647771

..5..49..167...1915...13271...117184....1142217.....9792821......87882289

..8..99..473...7556...81019..1142217...16510708...212408711....2962142231

.13.189.1205..29657..454822..9792821..212408711..4149393799...87858962506

.21.383.3161.123601.2647771.87882289.2962142231.87858962506.2858791588717

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>71

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A298775 A298582 A299574 * A299514 A299314 A300115

Adjacent sequences: A298393 A298394 A298395 * A298397 A298398 A298399

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 18 2018

Status

approved