login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)