A318946 Column 1 of triangle A318945.

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

Author

N. J. A. Sloane, Sep 18 2018

Keywords

• nonn
• more

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.

Crossrefs

Cf. A318945.

Programs

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

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)

Extensions

More terms from Peter Luschny, Oct 28 2018