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A295097
T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.
8
1, 2, 2, 3, 5, 3, 4, 11, 11, 4, 6, 24, 33, 24, 6, 9, 55, 114, 114, 55, 9, 13, 123, 377, 578, 377, 123, 13, 19, 276, 1249, 2859, 2859, 1249, 276, 19, 28, 621, 4151, 14187, 21185, 14187, 4151, 621, 28, 41, 1395, 13765, 70982, 158361, 158361, 70982, 13765, 1395, 41, 60
OFFSET
1,2
COMMENTS
Table starts
..1....2.....3.......4........6..........9..........13............19
..2....5....11......24.......55........123.........276...........621
..3...11....33.....114......377.......1249........4151.........13765
..4...24...114.....578.....2859......14187.......70982........353880
..6...55...377....2859....21185.....158361.....1182050.......8806229
..9..123..1249...14187...158361....1767431....19730839.....220211372
.13..276..4151...70982..1182050...19730839...329926211....5515740725
.19..621.13765..353880..8806229..220211372..5515740725..137994394960
.28.1395.45704.1763742.65681168.2459567704.92205260806.3452787904343
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-3)
k=2: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) -a(n-5)
k=3: [order 16]
k=4: [order 45]
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..1..1..0. .1..0..0..1. .1..1..1..0
..0..1..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..1. .0..1..0..0
..0..1..0..0. .1..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..1..0
..0..0..1..1. .0..1..0..0. .0..0..1..0. .0..1..1..0. .0..0..1..0
..0..0..0..0. .1..1..1..0. .0..0..1..0. .0..0..1..0. .1..1..0..0
CROSSREFS
Column 1 is A000930(n+1).
Sequence in context: A285935 A209568 A227641 * A295551 A196696 A196729
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 14 2017
STATUS
approved