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A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 3, 3, 3, 3, 0, 0, 2, 3, 3, 3, 2, 0, 0, 6, 8, 4, 4, 8, 6, 0, 0, 6, 16, 22, 32, 22, 16, 6, 0, 0, 11, 32, 39, 92, 92, 39, 32, 11, 0, 0, 16, 70, 102, 270, 366, 270, 102, 70, 16, 0, 0, 22, 135, 298, 1262, 1592, 1592, 1262, 298, 135, 22, 0, 0, 37, 293 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,17
COMMENTS
Table starts
.0..0..0...0....0.....0......0.......0........0.........0...........0
.0..1..1...1....3.....2......6.......6.......11........16..........22
.0..1..0...3....3.....8.....16......32.......70.......135.........293
.0..1..3...3....4....22.....39.....102......298.......833........2105
.0..3..3...4...32....92....270....1262.....3561.....13976.......48859
.0..2..8..22...92...366...1592....6925....36101....161645......762469
.0..6.16..39..270..1592..12042...75739...490425...3084820....19634393
.0..6.32.102.1262..6925..75739..729062..5841423..53750463...469053654
.0.11.70.298.3561.36101.490425.5841423.70536528.833035233.10021999204
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-4)
k=3: [order 14]
k=4: [order 43] for n>45
EXAMPLE
All solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..1..0..0. .0..1..1..0. .0..1..0..1. .0..0..1..0
..1..1..1..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
..0..0..1..0. .0..1..1..0. .1..0..1..0. .1..0..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1
CROSSREFS
Column 2 is A062200(n-2).
Sequence in context: A227827 A033700 A122916 * A132973 A107760 A180560
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 04 2018
STATUS
approved

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Last modified February 28 20:40 EST 2024. Contains 370400 sequences. (Running on oeis4.)