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A305649 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 6 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, 31, 31, 57, 13, 21, 125, 79, 137, 79, 125, 21, 34, 289, 168, 574, 574, 168, 289, 34, 55, 741, 430, 2360, 5547, 2360, 430, 741, 55, 89, 1737, 1241, 13498, 31079, 31079, 13498, 1241, 1737, 89, 144, 4045, 3577, 83190 (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...13.....31.......79........168..........430...........1241
..5...21...31....137......574.......2360........13498..........83190
..8...57...79....574.....5547......31079.......304707........3821570
.13..125..168...2360....31079.....355620......7215825......146459610
.21..289..430..13498...304707....7215825....283691091....10435409852
.34..741.1241..83190..3821570..146459610..10435409852...724085314967
.55.1737.3577.481377.37230262.2640107792.345636487600.42678601156125
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 54] for n>57
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..1..1. .0..0..0..1
..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0
..0..0..0..1. .0..0..0..0. .1..0..1..1. .0..0..1..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..1..0..0. .1..1..1..0. .1..0..0..1
..1..0..0..0. .0..0..0..1. .1..1..0..1. .0..1..1..1. .0..0..0..0
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A304349.
Sequence in context: A306172 A304355 A305918 * A316925 A305347 A316615
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 07 2018
STATUS
approved

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Last modified May 23 16:36 EDT 2024. Contains 372765 sequences. (Running on oeis4.)