A300427 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 30, 53, 30, 3, 5, 96, 272, 272, 96, 5, 8, 307, 1390, 2227, 1390, 307, 8, 13, 981, 7179, 18205, 18205, 7179, 981, 13, 21, 3137, 37042, 150352, 240196, 150352, 37042, 3137, 21, 34, 10034, 191135, 1240541, 3175101, 3175101

Offset

1,5

Comments

Table starts

..0.....1......1........2..........3............5..............8

..1.....3.....10.......30.........96..........307............981

..1....10.....53......272.......1390.........7179..........37042

..2....30....272.....2227......18205.......150352........1240541

..3....96...1390....18205.....240196......3175101.......41940055

..5...307...7179...150352....3175101.....67378450.....1429216222

..8...981..37042..1240541...41940055...1429216222....48707694395

.13..3137.191135.10232500..553858752..30305915964..1658695873019

.21.10034.986243.84410206.7314644478.642539662326.56476495490791

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7

k=3: [order 13] for n>14

k=4: [order 47] for n>49

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A055450 A185835 A301669 * A300689 A300612 A301354

Adjacent sequences: A300424 A300425 A300426 * A300428 A300429 A300430

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2018

Status

approved