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URL: https://oeis.org/A299806

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A299806
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 44, 44, 73, 32, 64, 157, 123, 174, 123, 157, 64, 128, 353, 343, 1059, 1059, 343, 353, 128, 256, 869, 973, 4543, 7013, 4543, 973, 869, 256, 512, 1993, 2774, 19006, 40015, 40015, 19006, 2774, 1993, 512, 1024
OFFSET
1,2
COMMENTS
Table starts
...1....2....4......8.......16........32..........64..........128
...2....7...13.....29.......73.......157.........353..........869
...4...13...20.....44......123.......343.........973.........2774
...8...29...44....174.....1059......4543.......19006........90935
..16...73..123...1059.....7013.....40015......265422......1763437
..32..157..343...4543....40015....388453.....3956148.....40566160
..64..353..973..19006...265422...3956148....61726046....969500658
.128..869.2774..90935..1763437..40566160...969500658..23457257837
.256.1993.7993.415860.11422152.419678087.15429018063.574690229422
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
k=3: [order 16] for n>17
k=4: [order 66] for n>70
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1
..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298215.
Sequence in context: A299097 A299879 A299015 * A299682 A300314 A280604
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 19 2018
STATUS
approved