Search: id:A088457
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%I A088457
%S A088457 1,0,1,2,4,8,18,44,113,296,782,2076,5538,14856,40100,108936,297793,
%T A088457 818832,2263481,6286498,17532707,49077268,137821247,388150322,
%U A088457 1095980561,3101840232,8797579789,25001305410,71179961918,203000438544
%N A088457 Number of single nodes (exactly one node on that level) for all Motzkin 
               paths of length n.
%e A088457 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 A088457 [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 A088457 (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))}
%Y A088457 Sequence in context: A059221 A114203 A100132 this_sequence A006786 A125809 
               A000117
%Y A088457 Adjacent sequences: A088454 A088455 A088456 this_sequence A088458 A088459 
               A088460
%K A088457 nonn
%O A088457 0,4
%A A088457 Michael Somos, Oct 01 2003

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