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.

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

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

R. H. Hardin, Table of n, a(n) for n = 1..220

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

Adjacent sequences: A316805 A316806 A316807 * A316809 A316810 A316811

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 14 2018

Status

approved