A378078 Number of noncrossing trees with n edges and all nodes having degree at most 3.

1, 1, 3, 12, 50, 219, 987, 4552, 21366, 101730, 490094, 2384520, 11699844, 57825103, 287611755, 1438536144, 7230782414, 36506547918, 185047345050, 941359362760, 4804468999932, 24593960996814, 126239765780606, 649610643221616, 3350542070046300, 17318377059738820

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

G.f.: (1 + g(x) + g(x)^2 + g(x)^3) where g(x)/x is the g.f. of A122871.

Example

a(4) = A001764(4) - 5 where the 5 trees excluded are those with one node connected to the other four.

Prog

(PARI) seq(n)={my(g=serreverse(x/(1+2*x+3*x^2) + O(x*x^n))); Vec(1 + g + g^2 + g^3)}

Crossrefs

Cf. A001764, A122871, A378079.

Sequence in context: A119976 A074547 A151178 * A151179 A191242 A105479

Adjacent sequences: A378075 A378076 A378077 * A378079 A378080 A378081

Keyword

nonn

Author

Andrew Howroyd, Nov 21 2024

Status

approved