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

Author

R. H. Hardin, Apr 12 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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).

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