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URL: https://oeis.org/A250162

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A250162
Number of length n+1 0..3 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
1
4, 20, 96, 436, 1880, 7836, 32032, 129572, 521256, 2091052, 8376368, 33529908, 134168632, 536772668, 2147287104, 8589541444, 34358952008, 137437380684, 549752668240, 2199016964180, 8796080439384, 35184346923100, 140737438023776
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).
Conjectures from Colin Barker, Nov 12 2018: (Start)
G.f.: 4*x*(1 - 3*x + 5*x^2) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).
a(n) = 2*(2 - 3*2^n + 4^n + 2*n).
(End)
EXAMPLE
Some solutions for n=6:
..1....3....3....2....3....2....2....2....2....1....1....2....1....0....2....1
..1....0....2....3....3....0....2....2....2....1....0....0....1....2....0....0
..0....3....1....3....3....2....3....3....2....3....3....0....1....2....3....2
..3....1....0....0....0....3....1....1....2....2....3....2....3....3....0....1
..0....2....3....3....3....2....3....2....1....0....1....3....3....1....2....2
..1....1....0....1....3....0....2....0....0....1....2....2....0....3....0....2
..3....3....1....2....3....2....2....0....2....3....1....0....1....2....2....3
CROSSREFS
Column 3 of A250167.
Sequence in context: A254943 A099025 A008353 * A296665 A057087 A151254
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved