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A299015
T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 6 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, 1052, 1052, 343, 353, 128, 256, 869, 957, 4488, 6908, 4488, 957, 869, 256, 512, 1993, 2710, 18758, 39124, 39124, 18758, 2710, 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.........957.........2710
...8...29...44....174.....1052......4488.......18758........89713
..16...73..123...1052.....6908.....39124......259556......1718835
..32..157..343...4488....39124....379236.....3848010.....39235328
..64..353..957..18758...259556...3848010....59666756....931277377
.128..869.2710..89713..1718835..39235328...931277377..22388413097
.256.1993.7749.409166.11081989.404291236.14739630633.545009501463
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..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0
..0..0..1..0. .1..1..1..1. .0..0..0..1. .0..1..1..0. .1..1..0..1
..0..0..1..1. .0..0..1..1. .0..0..1..0. .1..1..1..1. .0..0..0..1
..1..0..0..0. .1..0..1..1. .1..0..0..1. .0..0..0..0. .1..0..0..0
..1..0..1..1. .0..0..1..0. .0..1..1..0. .1..1..1..1. .1..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298215.
Sequence in context: A299350 A299097 A299879 * A299806 A299682 A300314
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 31 2018
STATUS
approved