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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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 05 2018
STATUS
approved