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A318946
Column 1 of triangle A318945.
1
0, 0, 0, 1, 5, 19, 64, 201, 603, 1752, 4973, 13871, 38176, 103985, 280947, 754216, 2014469, 5358823, 14209456, 37580841, 99188427, 261360696, 687777245, 1808000351, 4748806720, 12464634209, 32699621859, 85747477576, 224777691893, 589072137367, 1543445353168
OFFSET
0,5
LINKS
Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., Enumerations of peaks and valleys on non-decreasing Dyck paths, Discrete Mathematics (2018), 341(10), 2789-2807.
FORMULA
Conjectures from Colin Barker, Oct 28 2018: (Start)
G.f.: x^3*(1 - x)^2 / ((1 - 2*x)^2*(1 - 3*x + x^2)).
a(n) = 7*a(n-1) - 17*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>5.
(End)
MAPLE
a := n -> `if`(n < 2, 0, combinat:-fibonacci(2*n) - (n + 4)*2^(n - 3)):
seq(a(n), n=0..30); # Peter Luschny, Oct 28 2018
CROSSREFS
Cf. A318945.
Sequence in context: A049612 A211842 A304134 * A229239 A296330 A304162
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Sep 18 2018
EXTENSIONS
More terms from Peter Luschny, Oct 28 2018
STATUS
approved