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A317436
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 61, 45, 3, 5, 120, 201, 201, 120, 5, 8, 333, 863, 1140, 863, 333, 8, 13, 928, 3666, 6964, 6964, 3666, 928, 13, 21, 2613, 14831, 39216, 67214, 39216, 14831, 2613, 21, 34, 7400, 61638, 225065, 594763, 594763, 225065, 61638
OFFSET
1,5
COMMENTS
Table starts
..0....1......1.......2.........3...........5.............8.............13
..1....7.....16......45.......120.........333...........928...........2613
..1...16.....61.....201.......863........3666.........14831..........61638
..2...45....201....1140......6964.......39216........225065........1322225
..3..120....863....6964.....67214......594763.......5282805.......47791350
..5..333...3666...39216....594763.....8362442.....113897676.....1604462254
..8..928..14831..225065...5282805...113897676....2326497716....49910970516
.13.2613..61638.1322225..47791350..1604462254...49910970516..1648608723762
.21.7400.255772.7638732.429692708.22617426590.1074044399955.54927936213579
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
k=3: [order 20] for n>21
k=4: [order 68] for n>70
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..0
..1..0..0..1. .0..1..1..1. .1..0..1..1. .1..1..0..1. .1..1..1..0
..0..0..0..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..0..0..1
..0..0..1..1. .1..1..1..1. .0..0..0..1. .0..1..1..0. .0..1..1..0
..1..0..0..1. .0..1..1..0. .0..1..0..1. .1..1..1..1. .0..0..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A304013.
Sequence in context: A304697 A316448 A316130 * A303896 A305288 A304901
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 27 2018
STATUS
approved