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Search: id:A088457
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| A088457 |
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Number of single nodes (exactly one node on that level) for all Motzkin paths of length n. |
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+0
1
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| 1, 0, 1, 2, 4, 8, 18, 44, 113, 296, 782, 2076, 5538, 14856, 40100, 108936, 297793, 818832, 2263481, 6286498, 17532707, 49077268, 137821247, 388150322, 1095980561, 3101840232, 8797579789, 25001305410, 71179961918, 203000438544
(list; graph; listen)
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OFFSET
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0,4
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EXAMPLE
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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).
[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.
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PROGRAM
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(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))}
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CROSSREFS
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Sequence in context: A059221 A114203 A100132 this_sequence A006786 A125809 A000117
Adjacent sequences: A088454 A088455 A088456 this_sequence A088458 A088459 A088460
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 01 2003
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