A318343 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 20, 20, 16, 32, 42, 36, 36, 42, 32, 64, 89, 76, 67, 76, 89, 64, 128, 190, 160, 148, 148, 160, 190, 128, 256, 407, 344, 343, 393, 343, 344, 407, 256, 512, 873, 748, 817, 1115, 1115, 817, 748, 873, 512, 1024, 1874, 1624, 1975, 3321

Offset

1,2

Comments

Table starts

...1...2....4....8....16.....32......64......128.......256........512

...2...6...10...20....42.....89.....190......407.......873.......1874

...4..10...20...36....76....160.....344......748......1624.......3544

...8..20...36...67...148....343.....817.....1975......4788......11644

..16..42...76..148...393...1115....3321....10111.....30943......95244

..32..89..160..343..1115...4133...16267....66070....270320....1112195

..64.190..344..817..3321..16267...86487...476348...2647555...14797928

.128.407..748.1975.10111..66070..476348..3590263..27322989..209259065

.256.873.1624.4788.30943.270320.2647555.27322989.285034170.2994059337

Links

R. H. Hardin, Table of n, a(n) for n = 1..611

Formula

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) -2*a(n-4) +2*a(n-5) for n>6

k=4: [order 8] for n>9

k=5: [order 15] for n>18

k=6: [order 23] for n>27

k=7: [order 36] for n>41

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A317759.

Sequence in context: A097089 A317764 A318075 * A318024 A320409 A096466

Adjacent sequences: A318340 A318341 A318342 * A318344 A318345 A318346

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 24 2018

Status

approved