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A301361
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 34, 34, 37, 5, 8, 90, 92, 101, 92, 90, 8, 13, 223, 256, 320, 320, 256, 223, 13, 21, 550, 721, 1167, 1356, 1167, 721, 550, 21, 34, 1355, 2036, 3961, 6279, 6279, 3961, 2036, 1355, 34, 55, 3341, 5701, 13974, 30236, 44148
OFFSET
1,5
COMMENTS
Table starts
..0....1....1.....2......3........5.........8.........13...........21
..1....2....6....15.....37.......90.......223........550.........1355
..1....6...13....34.....92......256.......721.......2036.........5701
..2...15...34...101....320.....1167......3961......13974........49388
..3...37...92...320...1356.....6279.....30236.....147448.......713700
..5...90..256..1167...6279....44148....317019....2249565.....15884635
..8..223..721..3961..30236...317019...3241470...32453379....325518524
.13..550.2036.13974.147448..2249565..32453379..456790733...6500634810
.21.1355.5701.49388.713700.15884635.325518524.6500634810.132506438551
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +2*a(n-4) +a(n-5)
k=3: [order 31]
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..0. .0..0..1..1. .0..1..1..0. .0..1..1..0
..0..1..0..1. .1..1..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..0
..0..1..0..0. .1..1..1..0. .0..0..1..1. .1..1..0..0. .1..0..1..0
..1..0..0..1. .1..0..1..0. .0..0..0..0. .0..0..1..1. .1..0..1..0
..1..1..0..1. .0..0..1..0. .0..1..1..1. .1..1..0..0. .1..0..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A300344.
Sequence in context: A300435 A300769 A300639 * A267864 A336524 A219570
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 19 2018
STATUS
approved