A302741 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1637, 1652, 512, 32, 64, 2048, 11814, 21625, 11980, 2048, 64, 128, 8192, 85268, 285613, 286631, 86916, 8192, 128, 256, 32768, 615589, 3778433, 6947036, 3798398, 630604, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......228.......1637.........11814...........85268

...8....128.....1652......21625........285613.........3778433

..16....512....11980.....286631.......6947036.......168799572

..32...2048....86916....3798398.....168833401......7530280825

..64...8192...630604...50347423....4104946296....336148647504

.128..32768..4575332..667361051...99807877377..15005851329729

.256.131072.33196332.8845980434.2426739457531.669868217032865

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) = 7*a(n-1) +2*a(n-2) +2*a(n-3) -20*a(n-4) -16*a(n-5)

k=4: [order 15]

k=5: [order 46]

Empirical for row n:

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

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

n=3: a(n) = 7*a(n-1) +4*a(n-2) -17*a(n-3) -3*a(n-4) -9*a(n-6) +14*a(n-7) for n>8

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

n=5: [order 64] for n>65

Example

Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..0..0. .0..0..1..0
..1..0..0..0. .1..1..0..1. .0..0..1..0. .1..1..0..0. .1..1..1..1
..0..0..1..0. .1..1..0..1. .0..0..1..1. .0..1..1..1. .1..1..0..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: A299661 A320371 A317565 * A300215 A300804 A303456

Adjacent sequences: A302738 A302739 A302740 * A302742 A302743 A302744

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 12 2018

Status

approved