login
A303525
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 18, 10, 16, 13, 31, 37, 39, 21, 32, 21, 113, 80, 103, 95, 42, 64, 34, 363, 286, 359, 340, 246, 86, 128, 55, 813, 916, 1875, 1758, 1115, 687, 179, 256, 89, 1751, 2532, 8676, 13031, 9225, 4112, 2023, 370, 512, 144, 5001, 7477, 36072
OFFSET
1,2
COMMENTS
Table starts
...1...2....3.....5.......8........13.........21...........34............55
...2...3...11....21......31.......113........363..........813..........1751
...4...6...18....37......80.......286........916.........2532..........7477
...8..10...39...103.....359......1875.......8676........36072........166784
..16..21...95...340....1758.....13031......87730.......569770.......4036330
..32..42..246..1115....9225....102779....1052163.....10663440.....122173279
..64..86..687..4112...56046....965150...15768709....258412452....4730074082
.128.179.2023.16640..366415...9961980..260078546...6835357512..199276300520
.256.370.6126.71025.2519399.109395622.4544413190.190464446456.8858057538977
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 12] for n>15
k=4: [order 47] for n>49
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 58] for n>60
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..0..0
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .1..1..1..0
..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1. .1..0..1..0
..0..1..1..1. .0..1..1..0. .1..0..1..0. .0..1..1..1. .1..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.
Sequence in context: A302309 A303040 A302877 * A368643 A133948 A078935
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 25 2018
STATUS
approved