A301270 Number of labeled trees on n vertices containing two fixed non-adjacent edges.

4, 20, 144, 1372, 16384, 236196, 4000000, 77948684, 1719926784, 42417997492, 1157018619904, 34599023437500, 1125899906842624, 39618312131623748, 1499253470328324096, 60724508119499193196, 2621440000000000000000, 120167769980326767578964, 5829995856912430117421056, 298461883710362842247633948, 16079954871362414694843285504

Offset

4,1

Links

Table of n, a(n) for n=4..24.

M. Lavrov and M. Riedel, math.stackexchange.com, Number of labelled trees on n vertices containing two fixed non-adjacent edges

Formula

a(n) = 0 for n < 4, 4 * n^(n-4) = 4 * A008785(n-4) otherwise.

Example

The edges {1,2} and {3,4} can form a tree by being joined by an edge in four ways (two possibilities for each edge).

Mathematica

Array[4 #^(# - 4) &, 21, 4] (* Michael De Vlieger, Mar 19 2018 *)

Crossrefs

Cf. A000169, A000272, A008785.

Sequence in context: A160567 A034216 A144009 * A366183 A117887 A082988

Adjacent sequences: A301267 A301268 A301269 * A301271 A301272 A301273

Keyword

nonn

Author

Marko Riedel, Mar 17 2018

Status

approved