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A303197
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 12, 10, 16, 13, 25, 23, 23, 21, 32, 21, 65, 43, 46, 62, 42, 64, 34, 185, 105, 97, 185, 122, 86, 128, 55, 385, 233, 283, 523, 497, 305, 179, 256, 89, 649, 479, 687, 2106, 1751, 1357, 793, 370, 512, 144, 1489, 968, 1642, 7425, 8250, 5573
OFFSET
1,2
COMMENTS
Table starts
...1...2....3.....5.....8.....13......21.......34........55.........89
...2...3....9....17....25.....65.....185......385.......649.......1489
...4...6...12....23....43....105.....233......479.......968.......2146
...8..10...23....46....97....283.....687.....1642......3949......10169
..16..21...62...185...523...2106....7425....23976.....77199.....278516
..32..42..122...497..1751...8250...34801...138014....547379....2363422
..64..86..305..1357..5573..32223..164295...791150...3806973...20061588
.128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170
.256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370
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 7] for n>11
k=4: [order 42] for n>43
k=5: [order 33] for n>37
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: [order 18] for n>19
n=4: [order 70] for n>71
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..1
..1..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.
Sequence in context: A302163 A302635 A302427 * A059185 A302309 A303040
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 19 2018
STATUS
approved