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A316427 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 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, 53, 32, 32, 53, 13, 21, 105, 75, 97, 75, 105, 21, 34, 237, 148, 279, 279, 148, 237, 34, 55, 577, 311, 640, 1097, 640, 311, 577, 55, 89, 1205, 687, 1660, 2861, 2861, 1660, 687, 1205, 89, 144, 2681, 1443, 4353, 8761, 8916 (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
..2....5....9....21....53....105.....237......577.....1205......2681.......6349
..3....9...14....32....75....148.....311......687.....1443......3042.......6534
..5...21...32....97...279....640....1660.....4353....10975.....28038......72143
..8...53...75...279..1097...2861....8761....29548....87743....267014.....852011
.13..105..148...640..2861...8916...31433...121028...417457...1475614....5432803
.21..237..311..1660..8761..31433..130402...585212..2366785...9815061...42205654
.34..577..687..4353.29548.121028..585212..3242010.15459503..75494391..392102065
.55.1205.1443.10975.87743.417457.2366785.15459503.86620644.498441146.3054494072
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: [order 12]
k=4: [order 42] for n>43
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..0
..0..1..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..1
..1..1..0..1. .1..1..1..1. .1..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..0. .1..1..0..0. .0..1..0..0. .1..0..0..0
..1..1..1..1. .1..1..1..1. .1..1..1..0. .0..0..0..0. .0..0..0..0
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A303963.
Sequence in context: A316925 A305347 A316615 * A317429 A316239 A317160
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 02 2018
STATUS
approved

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Last modified February 24 05:36 EST 2024. Contains 370291 sequences. (Running on oeis4.)