Ways of placing n+1 labeled balls into 2 indistinguishable boxes with at least 2 balls in each box.
2^a(n) is an integer of the form 1/(2 - Sum_{i=1..m} i/2^i). -
Benoit Cloitre, Oct 25 2002
Number of permutations avoiding 13-2 that contain the pattern 23-1 exactly twice.
Cost of ternary maximum height Huffman tree with N internal nodes (non-leaves) for minimizing absolutely ordered sequences of size n = 2N + 1. - Alex Vinokur (alexvn(AT)barak-online.net), Nov 02 2004
a(n) is the number of Dyck n-paths whose third upstep initiates the last long ascent, n >= 1. A long ascent is one consisting of 2 or more upsteps. For example, a(3)=3 counts UUDuUDDD, UDUDuUDD, UUDDuUDD (third upstep in small type). -
David Callan, Dec 08 2004
Number of vertices of the tropical Grassmannian simplicial complex G(2,n), related to phylogenetic trees. -
Tom Copeland, Oct 03 2011
(Conjecture) Let a(2)=0. For n > 2, let N = 2*n + 1. For each n, define the n X n tridiagonal unit-primitive matrix (see [Jeffery]) A_{N,1}=[0,1,0,...,0; 1,0,1,0,...,0; 0,1,0,1,0,...,0; ...; 0,...,0,1,0,1; 0,...,0,1,1] associated with N. Define the n-dimensional column vectors V_N = [v_1,v_2,...,v_n]^T = [A_{N,1}]^n*[1,1,...,1]^T, where [.]^T denotes matrix transpose and [1,...,1] is the n-dimensional unit vector. Let (v_k)_N denote the k-th element of V_N, k in {1,...,n}. Then a(n) = (v_(n-2))_N. -
L. Edson Jeffery, Jan 20 2012
For n>2, a(n-2) is the number of connected induced (non-null) subgraphs of the n-centipede graph. -
Giovanni Resta, May 04 2017
a(n) is the number of maximal boundary strata of the moduli space of stable rational curves with n+1 marked points. The closures of the maximal boundary strata are called the irreducible boundary divisors of the moduli space; see Cavalieri Section 2.1. -
Harry Richman, Aug 13 2024
