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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 A128045

Adjacent sequences:  A268763 A268764 A268765 * A268767 A268768 A268769

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 13 2016

STATUS

approved

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Last modified May 22 19:19 EDT 2019. Contains 323481 sequences. (Running on oeis4.)