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A317043 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 57, 33, 33, 57, 13, 21, 125, 90, 141, 90, 125, 21, 34, 289, 204, 610, 610, 204, 289, 34, 55, 741, 527, 2516, 6188, 2516, 527, 741, 55, 89, 1737, 1547, 14294, 35318, 35318, 14294, 1547, 1737, 89, 144, 4045, 4509, 88030 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1....2....3......5........8.........13...........21.............34
..2....5....9.....21.......57........125..........289............741
..3....9...14.....33.......90........204..........527...........1547
..5...21...33....141......610.......2516........14294..........88030
..8...57...90....610.....6188......35318.......333207........4194626
.13..125..204...2516....35318.....393048......7760044......159647483
.21..289..527..14294...333207....7760044....302924053....11244564485
.34..741.1547..88030..4194626..159647483..11244564485...789775871803
.55.1737.4509.509381.41147020.2883656719.374107033198.46866337730606
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)
k=3: [order 17] for n>19
k=4: [order 52] for n>55
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..0..1. .0..1..1..0. .0..1..0..0
..0..1..1..1. .1..1..0..1. .1..1..0..0. .1..1..1..1. .0..0..0..0
..0..0..1..0. .0..0..1..0. .0..0..1..1. .1..1..1..1. .0..0..0..0
..1..1..0..1. .1..1..1..1. .1..1..0..0. .1..1..1..1. .0..0..0..0
..0..1..0..0. .1..0..1..1. .1..0..1..0. .1..0..1..1. .0..0..0..0
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A304349.
Sequence in context: A317429 A316239 A317160 * A317697 A132403 A209167
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 19 2018
STATUS
approved

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Last modified March 4 15:24 EST 2024. Contains 370532 sequences. (Running on oeis4.)