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A299879
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 7 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, 41, 41, 73, 32, 64, 157, 102, 125, 102, 157, 64, 128, 353, 253, 585, 585, 253, 353, 128, 256, 869, 632, 1974, 3068, 1974, 632, 869, 256, 512, 1993, 1563, 6542, 11263, 11263, 6542, 1563, 1993, 512, 1024, 4557
OFFSET
1,2
COMMENTS
Table starts
...1....2....4.....8......16.......32........64........128.........256
...2....7...13....29......73......157.......353........869........1993
...4...13...20....41.....102......253.......632.......1563........3896
...8...29...41...125.....585.....1974......6542......24545.......89192
..16...73..102...585....3068....11263.....53159.....246537.....1098723
..32..157..253..1974...11263....54005....324797....1859944....10716128
..64..353..632..6542...53159...324797...2714797...21236116...164681059
.128..869.1563.24545..246537..1859944..21236116..213883244..2166043717
.256.1993.3896.89192.1098723.10716128.164681059.2166043717.29310012663
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 67] for n>68
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..1. .0..1..1..0. .0..1..0..1. .0..1..0..0
..0..0..1..0. .1..1..0..0. .0..0..1..0. .1..0..1..0. .0..1..0..1
..1..1..1..0. .0..0..0..1. .1..1..1..1. .0..0..1..1. .1..1..1..1
..0..1..0..1. .1..0..1..0. .0..0..1..1. .0..0..1..1. .1..1..0..0
..1..1..0..1. .0..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298215.
Sequence in context: A298221 A299350 A299097 * A299015 A299806 A299682
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 21 2018
STATUS
approved