A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 169, 128, 16, 32, 384, 934, 1010, 512, 32, 64, 1405, 5117, 8718, 6084, 2048, 64, 128, 5135, 28128, 74072, 82367, 36456, 8192, 128, 256, 18766, 154494, 632004, 1089773, 773520, 218640, 32768, 256, 512, 68589, 848519

Offset

1,2

Comments

Table starts

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

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

...4.....32.....169.......934........5117.........28128..........154494

...8....128....1010......8718.......74072........632004.........5396562

..16....512....6084.....82367.....1089773......14458177.......192211013

..32...2048...36456....773520....15904814.....327603711......6769884156

..64...8192..218640...7267160...232260380....7428713676....238687785290

.128..32768.1312416..68346451..3396923500..168777255305...8434497360938

.256.131072.7873344.642498696.49653502029.3832039683236.297820640670676

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) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6

k=4: [order 18] for n>20

k=5: [order 90] for n>92

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 13] for n>15

n=4: [order 48] for n>50

Example

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

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: A301450 A302265 A302965 * A303469 A281955 A316183

Adjacent sequences: A302805 A302806 A302807 * A302809 A302810 A302811

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 13 2018

Status

approved