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A303325
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
10
1, 1, 2, 1, 2, 4, 1, 8, 1, 8, 1, 8, 4, 2, 16, 1, 32, 1, 8, 1, 32, 1, 32, 4, 2, 16, 2, 64, 1, 128, 1, 12, 4, 32, 1, 128, 1, 128, 4, 10, 64, 3, 64, 2, 256, 1, 512, 1, 46, 25, 62, 3, 128, 1, 512, 1, 512, 4, 50, 368, 56, 204, 10, 256, 2, 1024, 1, 2048, 1, 204, 201, 758, 136, 744, 9, 512, 1
OFFSET
1,3
COMMENTS
Table starts
...1.1...1..1...1....1.....1.....1.......1........1.........1..........1
...2.2...8..8..32...32...128...128.....512......512......2048.......2048
...4.1...4..1...4....1.....4.....1.......4........1.........4..........1
...8.2...8..2..12...10....46....50.....204......290......1034.......1682
..16.1..16..4..64...25...368...201....2545.....1855.....21082......17922
..32.2..32..3..62...56...758...822...11950....15100....206189.....274746
..64.1..64..3.204..136..2956..3929...69328...130531...2005898....4227664
.128.2.128.10.744..531.15494.24759..629227..1489177..33766564...89782726
.256.1.256..9.900.1035.44101.97205.3531980.11297739.359263250.1265799068
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-2)
k=3: a(n) = 2*a(n-1) for n>3
k=4: [order 55] for n>57
k=5: [order 33] for n>35
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 4*a(n-2)
n=3: a(n) = a(n-2)
n=4: [order 18] for n>19
n=5: [order 34] for n>35
EXAMPLE
All solutions for n=5 k=4
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 3 is A000079(n-1) for n>2.
Row 2 is A158302(n+1).
Row 3 is A010685(n+8).
Sequence in context: A157751 A177701 A119765 * A077901 A105619 A302212
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 21 2018
STATUS
approved