A378810 Number of horizontal steps in all peak and valleyless Motzkin meanders of length n.
0, 1, 4, 13, 39, 110, 300, 801, 2106, 5473, 14097, 36056, 91697, 232108, 585212, 1470557, 3684682, 9209417, 22967446, 57167993, 142051519, 352427720, 873157093, 2160579740, 5340150100, 13185150903, 32523933395, 80156852042, 197391001215, 485723767342
Offset: 0
Examples
For n = 3 we have meanders, UUU, UUH, UHU, UHD, HUU, UHH, HHU, HUH, HHH; giving a total of a(3) = 13 H steps.
Programs
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PARI
A088855(n,k) = {binomial(floor((n-1)/2), floor((k-1)/2))*binomial(ceil((n-1)/2),ceil((k-1)/2))} A_xy(N) = {my(x='x+O('x^N), h = sum(n=0,N, (1/(1-y*x)^(n+1)) * (if(n<1,1,0) + sum(k=1,n, A088855(n,k)*x^(n+k-1)*(y^(k-1)) )) )); h} P_xy(N) = Pol(A_xy(N), {x}) A_x(N) = {my(px = deriv(P_xy(N),y), y=1); Vecrev(eval(px))} A_x(20)
Formula
a(n) = Sum_{k=1..n} A378809(n,k)*k.
Comments