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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A320402 A208709 A300472 * A300811 A301450 A302265

Adjacent sequences: A326102 A326103 A326104 * A326106 A326107 A326108

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 06 2019

Status

approved