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A306060 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 27, 24, 16, 32, 64, 58, 58, 64, 32, 64, 184, 189, 164, 189, 184, 64, 128, 432, 526, 608, 608, 526, 432, 128, 256, 1088, 1344, 2168, 3572, 2168, 1344, 1088, 256, 512, 2944, 3772, 6955, 16833, 16833, 6955, 3772, 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....27....58.....189......526......1344.......3772.......10515
...8...24....58...164.....608.....2168......6955......23269.......80463
..16...64...189...608....3572....16833.....67791.....313348.....1479005
..32..184...526..2168...16833....99928....513811....3086539....18841620
..64..432..1344..6955...67791...513811...3363541...25699369...199805626
.128.1088..3772.23269..313348..3086539..25699369..257823074..2641827240
.256.2944.10515.80463.1479005.18841620.199805626.2641827240.35799252324
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 13] for n>14
k=4: [order 65] for n>67
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..1..1..0. .0..0..1..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..1..1
..1..0..0..0. .1..0..0..1. .1..1..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..0. .1..0..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A303794.
Sequence in context: A316304 A304848 A316545 * A317238 A260038 A193916
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 18 2018
STATUS
approved

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Last modified March 1 22:23 EST 2024. Contains 370443 sequences. (Running on oeis4.)