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A349408 Number of planar tanglegrams of size n. 2
1, 1, 2, 11, 76, 649, 6173, 63429, 688898, 7808246, 91537482, 1102931565, 13594564857, 170804438005, 2181426973452, 28257128116954, 370581034530685, 4913238656392058, 65773613137623085, 888155942037325535, 12086555915234897267, 165641209243876120135 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Alexander E. Black, Kevin Liu, Alex Mcdonough, Garrett Nelson, Michael C. Wigal, Mei Yin, and Youngho Yoo, Sampling planar tanglegrams and pairs of disjoint triangulations, arXiv:2304.05318 [math.CO], 2023.
Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana and Stephan Wagner, Counting Planar Tanglegrams, LIPIcs Proceedings of Analysis of Algorithms 2018, Vol. 110. Article 32.
FORMULA
G.f.: F(x) satisfies F(x) = H(F(x)) + x + (F(x)^2 + F(x^2))/2 where H(x)/x^2 is the g.f. of A257887.
EXAMPLE
For n=4, there are 11 planar tanglegrams of size 4.
PROG
(PARI) \\ here H(n)/x^2 is g.f. of A257887.
H(n)={(x - x^2 - serreverse(sum(k=0, n+1, (binomial(2*k, k)/(k+1))^2*x^(k+1)) + O(x^(n+3))))/2}
seq(n)={my(h=H(n-2), p=O(x)); for(n=1, n, p = subst(h + O(x*x^n), x, p) + x + (p^2 + subst(p, x, x^2))/2); Vec(p)} \\ Andrew Howroyd, Nov 18 2021
CROSSREFS
Row sums of A349409.
Sequence in context: A118802 A365146 A350680 * A053481 A368794 A110329
KEYWORD
nonn
AUTHOR
Kevin Liu, Nov 16 2021
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Nov 18 2021
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)