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A316545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 26, 24, 16, 32, 64, 53, 53, 64, 32, 64, 184, 187, 136, 187, 184, 64, 128, 432, 484, 568, 568, 484, 432, 128, 256, 1088, 1262, 1874, 4219, 1874, 1262, 1088, 256, 512, 2944, 3570, 5966, 19819, 19819, 5966, 3570, 2944, 512, 1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1....2....4.....8......16.......32........64........128..........256
...2....4...12....24......64......184.......432.......1088.........2944
...4...12...26....53.....187......484......1262.......3570.........9751
...8...24...53...136.....568.....1874......5966......20721........70789
..16...64..187...568....4219....19819.....85583.....452386......2248258
..32..184..484..1874...19819...114514....674392....4849500.....31884846
..64..432.1262..5966...85583...674392...5074646...49303976....433518999
.128.1088.3570.20721..452386..4849500..49303976..681913008...8395255440
.256.2944.9751.70789.2248258.31884846.433518999.8395255440.140688693646
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6
k=3: [order 11] for n>12
k=4: [order 34] for n>38
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
..1..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..1..0..0
..0..1..0..0. .0..1..1..0. .1..1..0..0. .1..1..1..0. .1..0..0..0
..0..0..0..0. .0..1..1..0. .0..0..0..0. .1..1..0..1. .0..0..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A303794.
Sequence in context: A304479 A316304 A304848 * A306060 A317238 A260038
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 06 2018
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)