A302965 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 154, 128, 16, 32, 384, 786, 833, 512, 32, 64, 1405, 3924, 6206, 4527, 2048, 64, 128, 5135, 19868, 43588, 49521, 24602, 8192, 128, 256, 18766, 100161, 314989, 493132, 395493, 133757, 32768, 256, 512, 68589, 505908

Offset: 1

Author

R. H. Hardin, Apr 16 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

...2......8......29.......105........384.........1405...........5135

...4.....32.....154.......786.......3924........19868.........100161

...8....128.....833......6206......43588.......314989........2257439

..16....512....4527.....49521.....493132......5122000.......52646395

..32...2048...24602....395493....5602382.....83644490.....1233435694

..64...8192..133757...3157171...63612987...1365216668....28906043997

.128..32768..727293..25208524..722646394..22301032112...677939939546

.256.131072.3954552.201291251.8212135689.364489574945.15913688413086

Examples

			Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..1..0. .0..0..1..0
..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..0..1..1. .1..0..1..0
..0..1..0..0. .1..1..1..1. .1..0..1..1. .0..1..0..0. .1..0..1..0
..1..1..1..1. .1..0..0..1. .1..0..1..0. .0..1..0..0. .1..0..1..1
..1..0..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .0..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 A302266.

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) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6

k=4: [order 19] for n>20

k=5: [order 80] for n>81

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)

n=3: [order 12] for n>13

n=4: [order 44] for n>45