A303456 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 232, 128, 16, 32, 512, 1690, 1696, 512, 32, 64, 2048, 12340, 22756, 12408, 2048, 64, 128, 8192, 90112, 306448, 306767, 90800, 8192, 128, 256, 32768, 658204, 4129588, 7626768, 4136339, 664512, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......232........1690.........12340...........90112

...8....128.....1696.......22756........306448.........4129588

..16....512....12408......306767.......7626768.......189848373

..32...2048....90800.....4136339.....189837638......8727953509

..64...8192...664512....55781418....4726484016....401405461699

.128..32768..4863312...752277525..117683035940..18461936404456

.256.131072.35593024.10145443043.2930192820802.849140799884830

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) = 8*a(n-1) -4*a(n-2) -2*a(n-3) -36*a(n-4) -16*a(n-5)

k=4: [order 15]

k=5: [order 47]

Empirical for row n:

n=1: a(n) = 2*a(n-1)

n=2: a(n) = 4*a(n-1)

n=3: a(n) = 8*a(n-1) -40*a(n-3) +20*a(n-4) +8*a(n-5) -3*a(n-6) +32*a(n-7) for n>8

n=4: [order 15] for n>16

n=5: [order 68] for n>69

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Row 2 is A004171(n-1).

Sequence in context: A302741 A300215 A300804 * A301443 A302010 A301784

Adjacent sequences: A303453 A303454 A303455 * A303457 A303458 A303459

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 24 2018

Status

approved