login
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.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 25 2018
STATUS
approved