A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 139, 128, 16, 32, 263, 678, 773, 512, 32, 64, 855, 3182, 5748, 4299, 2048, 64, 128, 2778, 15199, 39703, 48802, 23909, 8192, 128, 256, 9027, 72514, 281758, 496085, 414385, 132971, 32768, 256, 512, 29333, 346244

Offset

1,2

Comments

Table starts

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

...2......8......25........81.........263..........855...........2778

...4.....32.....139.......678........3182........15199..........72514

...8....128.....773......5748.......39703.......281758........1986213

..16....512....4299.....48802......496085......5240684.......54948498

..32...2048...23909....414385.....6196305.....97439921.....1518341751

..64...8192..132971...3518619....77396422...1812097252....41966406867

.128..32768..739525..29877293...966770632..33701001773..1159968653556

.256.131072.4112907.253694309.12076215811.626769301255.32062561937804

Links

R. H. Hardin, Table of n, a(n) for n = 1..417

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) -8*a(n-2) for n>3

k=4: a(n) = 13*a(n-1) -46*a(n-2) +72*a(n-3) -57*a(n-4) +16*a(n-5) for n>6

k=5: [order 11] for n>13

k=6: [order 25] for n>27

k=7: [order 53] for n>56

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6

n=3: [order 12] for n>14

n=4: [order 35] for n>38

n=5: [order 99] for n>104

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Sequence in context: A299359 A299180 A299942 * A302069 A298195 A299089

Adjacent sequences: A301838 A301839 A301840 * A301842 A301843 A301844

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 27 2018

Status

approved