A268766 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 1, 1, 2, 6, 2, 5, 15, 15, 5, 10, 44, 56, 44, 10, 20, 105, 223, 223, 105, 20, 38, 258, 762, 1148, 762, 258, 38, 71, 595, 2607, 5170, 5170, 2607, 595, 71, 130, 1368, 8500, 23156, 32056, 23156, 8500, 1368, 130, 235, 3069, 27411, 99057, 193573, 193573, 99057

Offset

1,4

Comments

Table starts

...0....1......2.......5........10.........20...........38............71

...1....6.....15......44.......105........258..........595..........1368

...2...15.....56.....223.......762.......2607.........8500.........27411

...5...44....223....1148......5170......23156........99057........418924

..10..105....762....5170.....32056.....193573......1129042.......6475898

..20..258...2607...23156....193573....1552272.....12111209......92571436

..38..595...8500...99057...1129042...12111209....127676872....1312123185

..71.1368..27411..418924...6475898...92571436...1312123185...18045771274

.130.3069..86622.1736105..36505596..696659613..13311824510..245588158242

.235.6830.270955.7122856.203462597.5178525870.133228716170.3292985469950

Links

R. H. Hardin, Table of n, a(n) for n = 1..1404

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6)

k=4: [order 8]

k=5: [order 12]

k=6: [order 16]

k=7: [order 28]

Example

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

Crossrefs

Column 1 is A001629.

Column 2 is A193449.

Sequence in context: A102912 A064850 A151853 * A214775 A196201 A342982

Adjacent sequences: A268763 A268764 A268765 * A268767 A268768 A268769

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2016

Status

approved