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A200840
Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases.
1
32, 191, 676, 1817, 4108, 8239, 15128, 25953, 42184, 65615, 98396, 143065, 202580, 280351, 380272, 506753, 664752, 859807, 1098068, 1386329, 1732060, 2143439, 2629384, 3199585, 3864536, 4635567, 5524876, 6545561, 7711652, 9038143
OFFSET
1,1
COMMENTS
Row 3 of A200838.
LINKS
FORMULA
Empirical: a(n) = (4/15)*n^5 + (17/6)*n^4 + (28/3)*n^3 + (73/6)*n^2 + (32/5)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(32 - x + 10*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
EXAMPLE
Some solutions for n=3
..2....1....1....1....2....3....1....0....0....0....2....2....1....1....2....3
..3....3....3....3....0....0....0....2....0....0....0....2....3....1....0....3
..0....3....0....0....0....1....3....2....2....3....0....0....1....2....3....2
..3....1....2....3....3....1....3....0....0....0....0....2....2....1....3....3
..0....2....0....2....0....0....1....0....2....0....0....0....2....3....0....2
CROSSREFS
Sequence in context: A306058 A317236 A233387 * A208925 A212863 A019560
KEYWORD
nonn
AUTHOR
R. H. Hardin Nov 23 2011
STATUS
approved