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.

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

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