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

Author

R. H. Hardin, Apr 13 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

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) = 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