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A316808 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 247, 128, 16, 32, 512, 1905, 1905, 512, 32, 64, 2048, 14711, 28248, 14711, 2048, 64, 128, 8192, 113606, 420345, 420345, 113606, 8192, 128, 256, 32768, 877309, 6256258, 12075849, 6256258, 877309, 32768, 256, 512, 131072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......247........1905.........14711...........113606
...8....128.....1905.......28248........420345..........6256258
..16....512....14711......420345......12075849........347046960
..32...2048...113606.....6256258.....347046960......19261290694
..64...8192...877309....93109949....9972851339....1068884675914
.128..32768..6774916..1385723098..286582122564...59316329979368
.256.131072.52318510.20623265507.8235306627639.3291689981719718
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -3*a(n-2) +7*a(n-3) -3*a(n-4)
k=4: a(n) = 15*a(n-1) -5*a(n-2) +50*a(n-3) -18*a(n-4) -81*a(n-5) +4*a(n-6) +20*a(n-7)
k=5: [order 22]
k=6: [order 59]
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..1..0. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..0..1..0. .0..0..0..0. .1..0..0..0
..0..1..1..1. .1..1..0..1. .1..1..0..1. .1..0..0..1. .1..0..1..1
..0..0..1..0. .1..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..0
..1..0..1..0. .1..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Sequence in context: A301443 A302010 A301784 * A299654 A317525 A300208
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 14 2018
STATUS
approved

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Last modified February 22 18:10 EST 2024. Contains 370260 sequences. (Running on oeis4.)