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A296578 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s. 8
2, 4, 4, 7, 11, 7, 13, 31, 31, 13, 24, 90, 135, 90, 24, 44, 254, 616, 616, 254, 44, 81, 728, 2782, 4543, 2782, 728, 81, 149, 2078, 12544, 32439, 32439, 12544, 2078, 149, 274, 5931, 56646, 233636, 368720, 233636, 56646, 5931, 274, 504, 16941, 255699, 1680927 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...2.....4.......7.......13.........24...........44.............81

...4....11......31.......90........254..........728...........2078

...7....31.....135......616.......2782........12544..........56646

..13....90.....616.....4543......32439.......233636........1680927

..24...254....2782....32439.....368720......4215593.......48217515

..44...728...12544...233636....4215593.....76657600.....1394258872

..81..2078...56646..1680927...48217515...1394258872....40337678992

.149..5931..255699.12090311..551193737..25339030733..1165868818808

.274.16941.1154239.86993766.6302520826.460672241848.33712843195488

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..311

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +4*a(n-2) +3*a(n-3) +a(n-4) +4*a(n-5) -a(n-6) -6*a(n-7) -a(n-8) +a(n-9)

k=3: [order 14]

k=4: [order 50]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000073(n+3).

Sequence in context: A282647 A269089 A282862 * A268750 A282996 A295275

Adjacent sequences:  A296575 A296576 A296577 * A296579 A296580 A296581

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 15 2017

STATUS

approved

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Last modified October 27 17:22 EDT 2021. Contains 348287 sequences. (Running on oeis4.)