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A305918 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 27, 27, 57, 13, 21, 125, 62, 101, 62, 125, 21, 34, 289, 135, 347, 347, 135, 289, 34, 55, 741, 312, 1129, 2014, 1129, 312, 741, 55, 89, 1737, 825, 4982, 8135, 8135, 4982, 825, 1737, 89, 144, 4045, 2367, 23181, 57465 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1....2....3......5.......8........13.........21...........34.............55
..2....5....9.....21......57.......125........289..........741...........1737
..3....9...13.....27......62.......135........312..........825...........2367
..5...21...27....101.....347......1129.......4982........23181.........101615
..8...57...62....347....2014......8135......57465.......489154........3344053
.13..125..135...1129....8135.....61467.....811996......9980597......112886453
.21..289..312...4982...57465....811996...18643274....371733699.....6830409319
.34..741..825..23181..489154...9980597..371733699..12581159370...364289254793
.55.1737.2367.101615.3344053.112886453.6830409319.364289254793.17019760656259
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 18] for n>20
k=4: [order 66] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1
..0..0..0..0. .1..1..1..0. .0..1..0..0. .0..1..1..1. .0..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..0. .1..1..1..1. .1..0..1..1
..0..0..0..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .0..1..0..0
..1..0..0..1. .1..0..1..1. .1..0..0..0. .1..1..1..0. .1..1..0..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A304349.
Sequence in context: A304669 A306172 A304355 * A305649 A316925 A305347
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 14 2018
STATUS
approved

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Last modified July 25 00:10 EDT 2024. Contains 374585 sequences. (Running on oeis4.)