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

1,2

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

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) -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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Row 2 is A302266.

Sequence in context: A300811 A301450 A302265 * A302808 A303469 A281955

Adjacent sequences: A302962 A302963 A302964 * A302966 A302967 A302968

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 16 2018

Status

approved