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A088457 Number of single nodes (exactly one node on that level) for all Motzkin paths of length n. 0

%I

%S 1,0,1,2,4,8,18,44,113,296,782,2076,5538,14856,40100,108936,297793,

%T 818832,2263481,6286498,17532707,49077268,137821247,388150322,

%U 1095980561,3101840232,8797579789,25001305410,71179961918,203000438544

%N Number of single nodes (exactly one node on that level) for all Motzkin paths of length n.

%e A Motzkin path of length n is a sequence [y(0),...,y(n)] such that |y(i)-y(i+1)|<=1, 0=y(0)=y(n)<=y(i).

%e [0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,1,2,1,0] are the a(4)=4 sequences.

%o (PARI) {a(n)=local(p0, p1, p2); if(n<0, 0, p1=1; polcoeff(sum(i=0, n, if(p2=(1-x)*p1-x^2*p0, p0=p1; p1=p2; (x^i/p0)^2), x*O(x^n)), n))}

%K nonn

%O 0,4

%A _Michael Somos_, Oct 01 2003

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)