%I #16 Jan 12 2020 11:28:03

%S 1,1,2,5,13,28,48,73,103,138,178,223,273,328,388,453,523,598,678,763,

%T 853,948,1048,1153,1263,1378,1498,1623,1753,1888,2028,2173,2323,2478,

%U 2638,2803,2973,3148,3328,3513,3703,3898,4098,4303,4513,4728,4948,5173,5403,5638

%N Number of Dyck paths of semilength n avoiding the pattern U^3 D^3 U D.

%H Colin Barker, <a href="/A225690/b225690.txt">Table of n, a(n) for n = 0..1000</a>

%H Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani and Julian West, <a href="http://dx.doi.org/10.1016/j.disc.2013.12.011">The Dyck pattern poset</a> Discrete Math. 321 (2014), 12--23. MR3154009.

%H A. Bernini, L. Ferrari, R. Pinzani and J. West, <a href="http://arxiv.org/abs/1303.3785">The Dyck pattern poset</a>, arXiv preprint arXiv:1303.3785, 2013

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = (5*n^2-15*n+6)/2 for n >= 4.

%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. - _Colin Barker_, Jul 10 2015

%F G.f.: (2*x^6-2*x^5-3*x^4-x^3-2*x^2+2*x-1) / (x-1)^3. - _Colin Barker_, Jul 10 2015

%o (PARI) Vec((2*x^6-2*x^5-3*x^4-x^3-2*x^2+2*x-1)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Jul 10 2015

%Y A row of A238095.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 27 2013