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A303040
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 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, 14, 10, 16, 13, 31, 28, 35, 21, 32, 21, 113, 56, 74, 71, 42, 64, 34, 363, 150, 234, 197, 186, 86, 128, 55, 813, 360, 869, 703, 544, 459, 179, 256, 89, 1751, 828, 2926, 3069, 2494, 1686, 1287, 370, 512, 144, 5001, 1906, 8500, 11079
OFFSET
1,2
COMMENTS
Table starts
...1...2....3.....5......8......13.......21........34.........55..........89
...2...3...11....21.....31.....113......363.......813.......1751........5001
...4...6...14....28.....56.....150......360.......828.......1906........4628
...8..10...35....74....234.....869.....2926......8500......27931.......96592
..16..21...71...197....703....3069....11079.....39281.....147655......574771
..32..42..186...544...2494...13597....59654....251705....1186522.....5869222
..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475
.128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879
.256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536
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 13] for n>16
k=4: [order 70]
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 11] for n>12
n=4: [order 61] for n>62
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
..0..0..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .1..1..0..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.
Sequence in context: A303197 A059185 A302309 * A302877 A303525 A368643
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 17 2018
STATUS
approved