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A296588
T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.
8
2, 3, 3, 5, 9, 5, 8, 22, 22, 8, 13, 62, 83, 62, 13, 21, 172, 346, 346, 172, 21, 34, 480, 1465, 2458, 1465, 480, 34, 55, 1358, 6241, 17503, 17503, 6241, 1358, 55, 89, 3849, 26895, 125765, 214830, 125765, 26895, 3849, 89, 144, 10951, 116541, 923475, 2607478
OFFSET
1,1
COMMENTS
Table starts
..2.....3......5........8.........13...........21.............34
..3.....9.....22.......62........172..........480...........1358
..5....22.....83......346.......1465.........6241..........26895
..8....62....346.....2458......17503.......125765.........923475
.13...172...1465....17503.....214830......2607478.......32689069
.21...480...6241...125765....2607478.....52756072.....1109882746
.34..1358..26895...923475...32689069...1109882746....39585589653
.55..3849.116541..6803610..410639937..23359296497..1408384872667
.89.10951.507102.50377421.5176790260.492457987101.50119033383361
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) -8*a(n-4) -3*a(n-6) -2*a(n-7) -5*a(n-8) +a(n-9)
k=3: [order 21]
k=4: [order 57]
EXAMPLE
Some solutions for n=4 k=4
..1..1..1..1. .0..1..0..1. .1..0..0..1. .0..1..0..0. .0..0..0..0
..1..0..1..0. .0..0..0..0. .0..1..0..0. .1..1..0..1. .0..0..0..1
..0..0..0..1. .0..0..0..0. .1..1..0..1. .0..1..0..0. .0..0..0..0
..0..0..0..0. .1..0..1..0. .0..1..1..1. .1..1..0..1. .0..0..1..0
CROSSREFS
Column 1 is A000045(n+2).
Sequence in context: A194000 A295781 A296725 * A065460 A241741 A175147
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 16 2017
STATUS
approved