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A280440
T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
7
0, 0, 0, 1, 4, 1, 2, 10, 10, 2, 5, 20, 21, 20, 5, 10, 38, 42, 42, 38, 10, 20, 68, 77, 80, 77, 68, 20, 38, 120, 136, 138, 138, 136, 120, 38, 71, 208, 236, 232, 225, 232, 236, 208, 71, 130, 358, 404, 386, 360, 360, 386, 404, 358, 130, 235, 612, 687, 640, 574, 548, 574, 640, 687
OFFSET
1,5
COMMENTS
Table starts
...0...0....1....2....5...10...20...38...71..130...235...420...744..1308..2285
...0...4...10...20...38...68..120..208..358..612..1042..1768..2992..5052..8514
...1..10...21...42...77..136..236..404..687.1162..1959..3294..5528..9262.15497
...2..20...42...80..138..232..386..640.1062.1764..2934..4884..8134.13548.22562
...5..38...77..138..225..360..574..920.1487.2422..3971..6542.10814.17914.29713
..10..68..136..232..360..548..834.1284.2008.3188..5128..8332.13638.22436.37032
..20.120..236..386..574..834.1211.1784.2684.4128..6478.10334.16693.27208.44620
..38.208..404..640..920.1284.1784.2512.3620.5360..8152.12692.20136.32400.52660
..71.358..687.1062.1487.2008.2684.3620.4989.7078.10365.15642.24224.38290.61451
.130.612.1162.1764.2422.3188.4128.5360.7078.9604.13474.19576.29384.45340.71490
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
k=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>6
k=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
k=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
k=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1
..0..1..0..1. .1..0..1..1. .1..0..1..0. .1..0..1..0. .0..0..1..0
..1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..0..1
..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1. .0..0..1..0
CROSSREFS
Column 1 is A001629(n-1).
Column 2 is A279262.
Sequence in context: A233528 A084604 A152253 * A024569 A206692 A159756
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2017
STATUS
approved