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A121482 Number of nondecreasing Dyck paths of semilength n and having no peaks at odd level (n>=0). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing. 2

%I #7 Jul 26 2022 11:54:21

%S 1,0,1,1,3,5,12,22,49,94,201,396,828,1656,3421,6899,14160,28686,58672,

%T 119156,243253,494688,1008860,2053168,4184892,8520248,17361293,

%U 35354517,72028485,146696143,298840769,608670551,1239888694,2525459305

%N Number of nondecreasing Dyck paths of semilength n and having no peaks at odd level (n>=0). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.

%C Column 0 of A121481.

%H E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, <a href="http://dx.doi.org/10.1016/S0012-365X(97)82778-1">Nondecreasing Dyck paths and q-Fibonacci numbers</a>, Discrete Math., 170, 1997, 211-217.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-2,-4,0,1).

%F G.f.: (1-z-z^2)(1-2z^2)/(1-z-4z^2+2z^3+4z^4-z^6).

%e a(4)=3 because we have UUDDUUDD, UUDUDUDD and UUUUDDDD, where U=(1,1) and D=(1,-1).

%p G:=(1-z-z^2)*(1-2*z^2)/(1-z-4*z^2+2*z^3+4*z^4-z^6): Gser:=series(G,z=0,40): seq(coeff(Gser,z,n),n=0..37);

%Y Cf. A121481.

%K nonn

%O 0,5

%A _Emeric Deutsch_, Aug 02 2006

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