A291887 Number of symmetrically unique Dyck paths of semilength n and height three.
1, 3, 11, 31, 91, 250, 690, 1863, 5017, 13389, 35621, 94354, 249352, 657421, 1730685, 4550031, 11950963, 31365810, 82274126, 215711947, 565376593, 1481448697, 3881041065, 10165822434, 26624745964, 69725071281, 182583838181, 478093234315, 1251829592839
Offset: 3
Links
- Alois P. Heinz, Table of n, a(n) for n = 3..1000
- Index entries for linear recurrences with constant coefficients, signature (6, -9, -8, 27, -10, -10, 4).
Crossrefs
Column k=3 of A291883.
Formula
G.f.: -x^3*(x^4+2*x^2-3*x+1)/((2*x-1)*(x^2-3*x+1)*(2*x^2-1)*(x^2+x-1)).