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A126220 Number of binary trees (i.e., rooted trees where each vertex has either 0, 1, or 2 children; and, when only one child is present, it is either a right child or a left child) with n edges and no adjacent vertices of outdegree 2. 1
1, 2, 5, 14, 40, 116, 344, 1040, 3188, 9880, 30912, 97520, 309856, 990656, 3184672, 10287808, 33379072, 108724864, 355405568, 1165521408, 3833497408, 12642775424, 41799227392, 138512751360, 459973953024, 1530498526208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = A126219(n,0), i.e., row 0 of triangle A126219.

G.f.: (1 - 2z - 4z^3 - sqrt(1 - 8z^3 + 4z^2 - 4z))/(8z^4).

Conjecture: (n+4)*a(n) +2*(-2*n-5)*a(n-1) +4*(n+1)*a(n-2) +4*(-2*n+1)*a(n-3)=0. - R. J. Mathar, Jun 17 2016

MAPLE

g:=(1-4*z^3-2*z-sqrt(1-8*z^3+4*z^2-4*z))/8/z^4: gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..30);

CROSSREFS

Cf. A126219.

Sequence in context: A036908 A293346 A273900 * A136304 A190254 A075496

Adjacent sequences:  A126217 A126218 A126219 * A126221 A126222 A126223

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 25 2006

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)