A326105 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 161, 108, 16, 32, 401, 929, 929, 401, 32, 64, 1490, 5383, 8628, 5383, 1490, 64, 128, 5536, 31236, 81088, 81088, 31236, 5536, 128, 256, 20569, 181227, 760989, 1233763, 760989, 181227, 20569, 256, 512, 76424, 1051456

Offset: 1

Author

R. H. Hardin, Jun 06 2019

Keywords

• nonn
• tabl

Comments

Table starts

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

...2.....8......29.......108.........401..........1490............5536

...4....29.....161.......929........5383.........31236..........181227

...8...108.....929......8628.......81088........760989.........7140349

..16...401....5383.....81088.....1233763......18773244.......285501774

..32..1490...31236....760989....18773244.....463572941.....11436374461

..64..5536..181227...7140349...285501774...11436374461....457515856087

.128.20569.1051456..67004116..4342306378..282167817331..18304957522469

.256.76424.6100399.628759699.66044562508.6962226034753.732434052866467

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

Formula

Empirical for column k:

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

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

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

k=4: [order 22]

k=5: [order 59] for n>60