A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 160, 108, 16, 32, 401, 925, 925, 401, 32, 64, 1490, 5363, 8608, 5363, 1490, 64, 128, 5536, 31106, 80914, 80914, 31106, 5536, 128, 256, 20569, 180397, 759100, 1231578, 759100, 180397, 20569, 256, 512, 76424, 1046223

Offset

1,2

Comments

Table starts

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

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

...4....29.....160.......925........5363.........31106..........180397

...8...108.....925......8608.......80914........759100.........7121067

..16...401....5363.....80914.....1231578......18735889.......284885784

..32..1490...31106....759100....18735889.....462538206.....11408562672

..64..5536..180397...7121067...284885784...11408562672....456303004550

.128.20569.1046223..66808673..4332278363..281433652906..18253046515989

.256.76424.6067629.626787854.65881928079.6942908646999.730219136878799

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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) = 6*a(n-1) -a(n-2) -a(n-3) +a(n-4) -4*a(n-5) +a(n-6) -a(n-7)

k=4: [order 22]

k=5: [order 58] for n>59

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A318016 A320402 A208709 * A326105 A300811 A301450

Adjacent sequences: A300469 A300470 A300471 * A300473 A300474 A300475

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 06 2018

Status

approved