0,2

The n-th term of the coordination sequence of the infinite tree with valency 2m is the same as the number of reduced words of size n in the free group on m generators. In the five sequences A003946, A003948, A003950, A003952, A003954 m is 2, 3, 4, 5, 6 . - Avi Peretz (njk(AT)netvision.net.il), Feb 23 2001 and Ola Veshta (olaveshta(AT)my-deja.com), Mar 30 2001.

Hamiltonian cycles in S_4 X P_2n.

For n>=1, a(n+1) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3,4,5,6} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3,4,5,6} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 10 2007

A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.

T. D. Noe, Table of n, a(n) for n=0..200

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

F. Faase, Counting Hamilton cycles in product graphs

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 307

Index entries for sequences related to trees

G.f.: (1+x)/(1-5x) - Paul Barry (pbarry(AT)wit.ie), Mar 28 2003

a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 4 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005

The Hankel transform of this sequence is [1,-6,0,0,0,0,0,0,0,0,...] - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

k := 6; if n = 0 then 1 else k*(k-1)^(n-1); fi;

Sequence in context: A001412 A006818 A006819 this_sequence A105488 A054117 A033132

Adjacent sequences: A003945 A003946 A003947 this_sequence A003949 A003950 A003951

nonn,easy,nice,walk

njas