A300115 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6, 7 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, 199, 515, 515, 199, 99, 13, 21, 189, 629, 2713, 3776, 2713, 629, 189, 21, 34, 383, 1837, 12669, 28935, 28935, 12669, 1837, 383, 34, 55, 777, 5397, 59569, 212470

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.......199.........629..........1837...........5397

..2..13...29....112......515......2713.......12669.........59569.........295903

..3..23...63....515.....3776.....28935......212470.......1560065.......11874071

..5..49..199...2713....28935....346593.....4293657......52304635......651028308

..8..99..629..12669...212470...4293657....87633085....1730369641....35186245661

.13.189.1837..59569..1560065..52304635..1730369641...55075362479..1818989406366

.21.383.5397.295903.11874071.651028308.35186245661.1818989406366.98018916520293

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 16] for n>17

k=4: [order 56] for n>60

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A298396 A299514 A299314 * A100888 A322469 A052914

Adjacent sequences: A300112 A300113 A300114 * A300116 A300117 A300118

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 25 2018

Status

approved