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Column 1 of triangle A318945.
1

%I #11 Oct 28 2018 20:47:11

%S 0,0,0,1,5,19,64,201,603,1752,4973,13871,38176,103985,280947,754216,

%T 2014469,5358823,14209456,37580841,99188427,261360696,687777245,

%U 1808000351,4748806720,12464634209,32699621859,85747477576,224777691893,589072137367,1543445353168

%N Column 1 of triangle A318945.

%H Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., <a href="https://doi.org/10.1016/j.disc.2018.06.032">Enumerations of peaks and valleys on non-decreasing Dyck paths</a>, Discrete Mathematics (2018), 341(10), 2789-2807.

%F Conjectures from _Colin Barker_, Oct 28 2018: (Start)

%F G.f.: x^3*(1 - x)^2 / ((1 - 2*x)^2*(1 - 3*x + x^2)).

%F a(n) = 7*a(n-1) - 17*a(n-2) + 16*a(n-3) - 4*a(n-4) for n>5.

%F (End)

%p a := n -> `if`(n < 2, 0, combinat:-fibonacci(2*n) - (n + 4)*2^(n - 3)):

%p seq(a(n), n=0..30); # _Peter Luschny_, Oct 28 2018

%Y Cf. A318945.

%K nonn,more

%O 0,5

%A _N. J. A. Sloane_, Sep 18 2018

%E More terms from _Peter Luschny_, Oct 28 2018