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A088457 Number of single nodes (exactly one node on that level) for all Motzkin paths of length n. 0
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; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

EXAMPLE

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.

PROG

(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))}

CROSSREFS

Sequence in context: A114203 A100132 A176720 * A006786 A125809 A245176

Adjacent sequences:  A088454 A088455 A088456 * A088458 A088459 A088460

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 01 2003

STATUS

approved

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Last modified February 26 21:50 EST 2020. Contains 332295 sequences. (Running on oeis4.)