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%I A243414 #7 Jun 05 2014 05:33:22
%S A243414 1,7,34,149,627,2584,10529,42606,171563,688255,2752912,10985005,
%T A243414 43747708,173937910,690592594,2738547328,10848121023,42931655341,
%U A243414 169759128539,670744883641,2648384384709,10450336782375,41212385684767,162440029038575,639946101535124
%N A243414 Number of Dyck paths of semilength n having exactly 2 (possibly overlapping) occurrences of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)).
%H A243414 Alois P. Heinz, <a href="/A243414/b243414.txt">Table of n, a(n) for n = 6..550</a>
%H A243414 Vaclav Kotesovec, <a href="/A243414/a243414.txt">Recurrence (of order 10)</a>
%F A243414 a(n) ~ c * d^n * sqrt(n), where d = 3.8821590268628506747194368909643384... (same as for A243412) is the root of the equation d^8 - 2*d^7 - 10*d^6 + 12*d^5 - 5*d^4 - 2*d^3 - 5*d^2 - 8*d - 3 = 0, and c = 0.000227236615409194082906635273578... . - _Vaclav Kotesovec_, Jun 05 2014
%Y A243414 Column k=2 of A243366.
%K A243414 nonn
%O A243414 6,2
%A A243414 _Alois P. Heinz_, Jun 04 2014

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