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A316925 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 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, 31, 31, 57, 13, 21, 125, 81, 137, 81, 125, 21, 34, 289, 184, 594, 594, 184, 289, 34, 55, 741, 492, 2574, 6339, 2574, 492, 741, 55, 89, 1737, 1457, 15118, 40938, 40938, 15118, 1457, 1737, 89, 144, 4045, 4371, 95244 (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.......81........184..........492............1457
..5...21...31....137......594.......2574........15118...........95244
..8...57...81....594.....6339......40938.......428394.........5627600
.13..125..184...2574....40938.....533726.....11571636.......256609365
.21..289..492..15118...428394...11571636....493774680.....20147703090
.34..741.1457..95244..5627600..256609365..20147703090...1580858618327
.55.1737.4371.569635.59111561.5035506864.740128547549.105913781465166
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 51] for n>55
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..1..0..0. .0..0..1..1. .0..1..1..0
..0..0..1..1. .1..0..0..0. .1..1..0..1. .0..0..0..1. .1..1..1..1
..1..1..0..0. .0..0..0..0. .1..1..1..1. .1..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..0..0. .1..1..1..1. .1..0..0..0. .0..1..1..0
..0..1..0..1. .0..1..0..0. .1..1..1..1. .0..0..0..1. .1..1..1..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A304349.
Sequence in context: A304355 A305918 A305649 * A305347 A316615 A316427
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 16 2018
STATUS
approved

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Last modified April 18 09:35 EDT 2024. Contains 371779 sequences. (Running on oeis4.)