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A296335
T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.
8
2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 47, 64, 47, 13, 21, 116, 230, 230, 116, 21, 34, 286, 816, 1235, 816, 286, 34, 55, 705, 2895, 6504, 6504, 2895, 705, 55, 89, 1738, 10277, 34224, 50595, 34224, 10277, 1738, 89, 144, 4285, 36480, 180404, 392230, 392230, 180404
OFFSET
1,1
COMMENTS
Table starts
..2....3......5.......8........13.........21...........34............55
..3....8.....19......47.......116........286..........705..........1738
..5...19.....64.....230.......816.......2895........10277.........36480
..8...47....230....1235......6504......34224.......180404........950451
.13..116....816....6504.....50595.....392230......3051494......23717411
.21..286...2895...34224....392230....4476519.....51335713.....587914968
.34..705..10277..180404...3051494...51335713....869077778...14686634221
.55.1738..36480..950451..23717411..587914968..14686634221..366077961514
.89.4285.129486.5007796.184355308.6733523523.248214082895.9126072558650
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: a(n) = 2*a(n-1) +4*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-9)
k=4: [order 21]
k=5: [order 44]
EXAMPLE
Some solutions for n=5 k=4
..1..0..0..1. .0..0..1..0. .1..0..1..1. .0..0..1..1. .1..1..0..1
..0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..1..0. .1..0..0..0
..0..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..0
..1..0..0..0. .1..0..0..0. .0..1..0..1. .1..1..0..0. .1..0..0..0
CROSSREFS
Column 1 is A000045(n+2).
Sequence in context: A053218 A198335 A339050 * A296635 A295051 A295379
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 10 2017
STATUS
approved