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A303969 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 5 king-move adjacent elements, with upper left element zero. 8
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 53, 26, 26, 53, 13, 21, 105, 54, 73, 54, 105, 21, 34, 237, 101, 173, 173, 101, 237, 34, 55, 577, 186, 374, 452, 374, 186, 577, 55, 89, 1205, 361, 842, 1014, 1014, 842, 361, 1205, 89, 144, 2681, 700, 1923, 2247, 2597, 2247 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1....2...3....5.....8....13.....21.....34.....55......89.....144......233
..2....5...9...21....53...105....237....577...1205....2681....6349....13681
..3....9..13...26....54...101....186....361....700....1340....2562.....4913
..5...21..26...73...173...374....842...1923...4326....9786...22216....50282
..8...53..54..173...452..1014...2247...5247..11995...27818...65183...151096
.13..105.101..374..1014..2597...6264..16205..40375..105045..275549...708306
.21..237.186..842..2247..6264..15517..40239.101894..275913..742329..1970215
.34..577.361.1923..5247.16205..40239.112219.300835..906290.2653885..7634900
.55.1205.700.4326.11995.40375.101894.300835.872394.2901626.9125913.28392355
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)
k=3: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) +a(n-5) +a(n-6) -a(n-7) -a(n-11) -a(n-12)
k=4: [order 36] for n>37
k=5: [order 24] for n>35
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
..1..1..1..1. .1..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..0. .1..0..0..0. .0..0..0..0
..0..1..1..0. .1..0..1..1. .1..0..0..1. .1..1..0..0. .1..0..0..0
CROSSREFS
Column 1 is A000045(n+1).
Sequence in context: A202874 A355197 A199512 * A304931 A304669 A306172
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 03 2018
STATUS
approved

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Last modified May 30 17:56 EDT 2024. Contains 372971 sequences. (Running on oeis4.)