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A317125
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 82, 65, 16, 32, 192, 302, 302, 192, 32, 64, 569, 1164, 1597, 1164, 569, 64, 128, 1709, 4561, 8598, 8598, 4561, 1709, 128, 256, 5162, 17966, 46955, 65099, 46955, 17966, 5162, 256, 512, 15663, 70913, 258241, 507378, 507378
OFFSET
1,2
COMMENTS
Table starts
...1.....2......4.......8........16.........32...........64............128
...2.....8.....23......65.......192........569.........1709...........5162
...4....23.....82.....302......1164.......4561........17966..........70913
...8....65....302....1597......8598......46955.......258241........1422755
..16...192...1164....8598.....65099.....507378......3982123.......31333222
..32...569...4561...46955....507378....5694906.....64566869......734571604
..64..1709..17966..258241...3982123...64566869...1062867065....17593640188
.128..5162..70913.1422755..31333222..734571604..17593640188...424977120539
.256.15663.280153.7843425.246848528.8373046468.292154717629.10317078557668
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5
k=3: [order 16]
k=4: [order 57] for n>59
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
..0..0..0..0. .0..1..1..1. .1..0..0..0. .0..0..0..1. .0..0..1..1
..0..0..1..1. .0..1..1..1. .0..0..1..1. .1..0..0..0. .0..0..0..1
..0..0..1..1. .1..0..1..1. .0..0..1..1. .1..1..0..0. .1..0..1..1
..1..0..0..0. .1..1..1..0. .0..0..0..0. .1..1..1..0. .0..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A304304.
Sequence in context: A304310 A316209 A305776 * A305593 A317011 A316876
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 21 2018
STATUS
approved