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A297374 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s. 13
2, 4, 4, 8, 16, 8, 16, 57, 64, 16, 32, 208, 393, 256, 32, 64, 765, 2610, 2719, 1024, 64, 128, 2807, 17534, 33054, 18805, 4096, 128, 256, 10294, 116932, 409507, 418344, 130063, 16384, 256, 512, 37759, 780273, 4986469, 9554038, 5294713, 899565, 65536, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

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

...4.....16.......57.........208...........765............2807

...8.....64......393........2610.........17534..........116932

..16....256.....2719.......33054........409507.........4986469

..32...1024....18805......418344.......9554038.......211988289

..64...4096...130063.....5294713.....222925151......9012089653

.128..16384...899565....67012245....5201484239....383128155296

.256..65536..6221735...848136217..121365562862..16287817972455

.512.262144.43031893.10734382366.2831807366510.692439110062325

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..541

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) -4*a(n-3)

k=4: a(n) = 13*a(n-1) -4*a(n-2) -3*a(n-3) -19*a(n-4) +15*a(n-5) -a(n-6)

k=5: [order 9] for n>11

k=6: [order 17] for n>19

k=7: [order 28] for n>31

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) +5*a(n-3) +a(n-4) +a(n-5) -a(n-6) -a(n-7)

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

n=4: [order 29] for n>31

n=5: [order 84] for n>87

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0

..1..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0

..1..0..1..0. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..1..1..1

..1..0..0..0. .1..0..0..1. .0..1..0..0. .1..0..1..1. .0..0..1..0

..0..0..0..0. .0..0..1..1. .0..1..0..0. .1..0..0..1. .0..0..1..1

CROSSREFS

Column 1 is A000079.

Column 2 is A000302.

Row 1 is A000079.

Sequence in context: A283130 A295716 A282399 * A297102 A283415 A283857

Adjacent sequences:  A297371 A297372 A297373 * A297375 A297376 A297377

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 29 2017

STATUS

approved

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Last modified January 24 10:22 EST 2020. Contains 331193 sequences. (Running on oeis4.)