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A304855
T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 3, 4 or 7 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 35, 15, 15, 35, 13, 21, 61, 29, 38, 29, 61, 21, 34, 127, 51, 65, 65, 51, 127, 34, 55, 265, 91, 127, 148, 127, 91, 265, 55, 89, 507, 177, 264, 334, 334, 264, 177, 507, 89, 144, 1013, 363, 626, 731, 762, 731, 626, 363, 1013
OFFSET
1,2
COMMENTS
Table starts
..1...2...3....5....8....13....21.....34......55......89......144.......233
..2...5...7...17...35....61...127....265.....507....1013.....2071......4097
..3...7...9...15...29....51....91....177.....363.....739.....1513......3143
..5..17..15...38...65...127...264....626....1369....3086.....7163.....16749
..8..35..29...65..148...334...731...1921....5171...14195....38242....106896
.13..61..51..127..334...762..2073...6400...19099...57502...177379....558534
.21.127..91..264..731..2073..6750..23642...80209..281982..1002046...3608377
.34.265.177..626.1921..6400.23642..97917..380399.1537086..6286402..25733269
.55.507.363.1369.5171.19099.80209.380399.1725334.7992738.37459484.176294209
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2);
k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n > 5;
k=3: [order 12];
k=4: [order 41] for n > 44.
EXAMPLE
Some solutions for n=5, k=4
..0..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..1..1
..0..0..0..0. .0..0..0..0. .1..0..0..1. .0..0..0..0. .1..1..1..1
..1..0..0..0. .0..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..1..1
..1..1..0..0. .0..0..0..1. .1..1..0..0. .0..0..0..0. .1..1..1..1
..1..1..1..0. .0..0..1..1. .1..0..0..0. .0..0..0..0. .1..0..0..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A303802.
Sequence in context: A303682 A304133 A303808 * A304544 A306129 A304221
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 19 2018
STATUS
approved