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

Author

R. H. Hardin, Aug 24 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A317759.

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