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A303084 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 32, 3, 16, 1, 72, 29, 112, 6, 32, 1, 168, 258, 90, 416, 10, 64, 1, 496, 432, 1455, 304, 1512, 21, 128, 1, 1296, 2525, 3667, 11767, 1054, 5472, 42, 256, 1, 3616, 6313, 33152, 34430, 84474, 4182, 19904, 86, 512, 1, 9760, 30188, 157838 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
...1..1.....1.....1........1.........1............1.............1
...2..2....12....20.......72.......168..........496..........1296
...4..2....32....29......258.......432.........2525..........6313
...8..3...112....90.....1455......3667........33152........157838
..16..6...416...304....11767.....34430.......636070.......4585419
..32.10..1512..1054....84474....409478.....13375327.....170974652
..64.21..5472..4182...615471...4862916....266882021....5924274499
.128.42.19904.17369..4647197..60442630...5754725245..218955384065
.256.86.72396.75377.35089147.764631608.125608726910.8100166904419
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 11]
k=4: [order 56] for n>57
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 17] for n>18
n=4: [order 67] for n>68
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..1
..0..0..0..1. .1..1..1..1. .0..0..1..1. .1..1..1..1. .1..0..0..1
..0..1..0..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .1..0..0..1
..0..0..0..0. .0..0..0..0. .1..0..0..1. .1..1..1..1. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .1..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A302368.
Sequence in context: A302460 A303242 A302367 * A302889 A303624 A121439
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 18 2018
STATUS
approved

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)