A316960 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 220, 128, 16, 32, 512, 1498, 1498, 512, 32, 64, 2048, 10243, 16976, 10243, 2048, 64, 128, 8192, 70037, 194917, 194917, 70037, 8192, 128, 256, 32768, 478941, 2232443, 3796326, 2232443, 478941, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

...1......2........4..........8...........16.............32................64

...2......8.......32........128..........512...........2048..............8192

...4.....32......220.......1498........10243..........70037............478941

...8....128.....1498......16976.......194917........2232443..........25592081

..16....512....10243.....194917......3796326.......73529753........1426910760

..32...2048....70037....2232443.....73529753.....2402722112.......78728223139

..64...8192...478941...25592081...1426910760....78728223139.....4359094468163

.128..32768..3275421..293396247..27687032205..2579211359302...241311689147759

.256.131072.22400407.3363774685.537290478883.84510945441118.13360998189431905

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

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) = 6*a(n-1) +9*a(n-2) -14*a(n-3) -52*a(n-4) -33*a(n-5) for n>6

k=4: [order 16] for n>17

k=5: [order 58] for n>59

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .1..0..0..0. .0..1..1..1. .1..0..0..1. .1..0..1..1
..0..0..1..0. .1..1..1..1. .1..1..1..0. .1..1..0..1. .1..0..1..1
..1..1..0..0. .0..1..1..1. .1..1..1..0. .0..1..0..0. .0..0..0..1
..1..1..1..1. .0..1..0..0. .0..1..1..1. .0..0..1..0. .0..0..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A300259 A305523 A298970 * A299740 A316815 A299661

Adjacent sequences: A316957 A316958 A316959 * A316961 A316962 A316963

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 17 2018

Status

approved