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A253122 Number of length n+2 0..1 arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero. 1
4, 12, 16, 40, 64, 144, 256, 544, 1024, 2112, 4096, 8320, 16384, 33024, 65536, 131584, 262144, 525312, 1048576, 2099200, 4194304, 8392704, 16777216, 33562624, 67108864, 134234112, 268435456, 536903680, 1073741824, 2147549184, 4294967296 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3).
Conjectures from Colin Barker, Dec 09 2018: (Start)
G.f.: 4*x*(1 + x - 4*x^2) / ((1 - 2*x)*(1 - 2*x^2)).
a(n) = 2^(n/2+1) + 2^(n+1) for n even.
a(n) = 2^(n+1) for n odd.
(End)
EXAMPLE
Some solutions for n=10:
..1....1....0....0....0....0....0....1....0....1....0....0....0....1....1....0
..1....1....1....0....1....1....1....1....1....0....0....0....1....1....0....1
..0....0....1....0....1....0....1....0....1....0....0....0....1....1....0....1
..1....0....0....1....0....0....1....1....1....1....1....0....0....1....0....1
..0....0....0....0....0....0....1....1....0....0....0....0....0....1....0....0
..1....0....1....0....1....0....1....0....1....1....1....0....0....1....0....1
..0....1....1....1....0....0....0....0....0....0....1....0....0....0....0....1
..0....0....0....0....0....0....1....0....0....0....0....0....1....1....1....1
..1....0....0....1....0....1....1....0....1....1....1....0....0....1....0....1
..0....1....0....0....0....1....1....1....1....0....0....0....0....1....0....0
..1....0....0....1....1....0....0....1....0....1....1....1....0....1....0....0
..0....1....1....0....0....0....1....1....0....0....1....0....0....1....0....0
CROSSREFS
Column 1 of A253129.
Sequence in context: A291781 A348342 A348273 * A239413 A351893 A327295
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 27 2014
STATUS
approved

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)