A320409 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 6, 4, 8, 14, 14, 8, 16, 35, 47, 35, 16, 32, 95, 156, 156, 95, 32, 64, 257, 548, 786, 548, 257, 64, 128, 700, 1970, 3761, 3761, 1970, 700, 128, 256, 1907, 7049, 18725, 27236, 18725, 7049, 1907, 256, 512, 5202, 25364, 92578, 191615, 191615, 92578

Offset

1,2

Comments

Table starts

...1....2.....4.......8.......16.........32..........64...........128

...2....6....14......35.......95........257.........700..........1907

...4...14....47.....156......548.......1970........7049.........25364

...8...35...156.....786.....3761......18725.......92578........463045

..16...95...548....3761....27236.....191615.....1353623.......9623424

..32..257..1970...18725...191615....1957026....19677729.....199877194

..64..700..7049...92578..1353623...19677729...282206549....4085687781

.128.1907.25364..463045..9623424..199877194..4085687781...84346447443

.256.5202.91307.2308299.68454701.2025592349.58997871413.1737667793009

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 23] for n>25

k=4: [order 83] for n>85

Example

Some solutions for n=5 k=4
..0..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .1..0..0..1
..0..1..0..0. .1..0..0..1. .1..1..1..1. .1..0..1..1. .0..0..0..0
..1..0..1..0. .1..1..1..1. .0..0..0..0. .0..1..0..1. .0..0..1..0
..1..1..0..0. .1..1..0..1. .0..0..0..1. .0..0..0..1. .0..1..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A318018.

Sequence in context: A318075 A318343 A318024 * A096466 A088965 A059474

Adjacent sequences: A320406 A320407 A320408 * A320410 A320411 A320412

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 12 2018

Status

approved