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A317011
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 96, 65, 16, 32, 192, 400, 400, 192, 32, 64, 569, 1704, 2567, 1704, 569, 64, 128, 1709, 7313, 16048, 16048, 7313, 1709, 128, 256, 5162, 31328, 101054, 147281, 101054, 31328, 5162, 256, 512, 15663, 134118, 639838, 1372782
OFFSET
1,2
COMMENTS
Table starts
...1.....2......4........8.........16..........32............64.............128
...2.....8.....23.......65........192.........569..........1709............5162
...4....23.....96......400.......1704........7313.........31328..........134118
...8....65....400.....2567......16048......101054........639838.........4056201
..16...192...1704....16048.....147281.....1372782......12838095.......120108770
..32...569...7313...101054....1372782....19006132.....263269309......3646120276
..64..1709..31328...639838...12838095...263269309....5395769696....110527120611
.128..5162.134118..4056201..120108770..3646120276..110527120611...3348077796513
.256.15663.574442.25720439.1124195594.50524538223.2265876477133.101540680029955
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] for n>17
k=4: [order 57] for n>59
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..0..0
..0..1..0..0. .1..1..0..0. .1..1..0..1. .0..0..1..1. .0..0..0..0
..0..0..0..0. .1..1..0..1. .0..1..1..0. .1..1..1..1. .1..1..0..0
..0..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..1..1. .1..0..0..0
..1..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..1. .1..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A304304.
Sequence in context: A305776 A317125 A305593 * A316876 A317604 A038208
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 18 2018
STATUS
approved