%I A058366
%S A058366 1,1,1,1,1,1,8,9,10,11,12,13,14,22,31,41,52,64,77,91,113,144,185,237,
%T A058366 301,378,469,582,726,911,1148,1449,1827,2296,2878,3604,4515,5663,7112,
%U A058366 8939,11235,14113,17717,22232,27895,35007,43946,55181,69294,87011
%N A058366 Number of ways to cover (without overlapping) a ring lattice (necklace) 
               of n sites with molecules that are 7 sites wide.
%C A058366 This comment covers a family of sequences which satisfy a recurrence 
               of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 1...m-1, 
               a(m) = m+1. The generating function is (x+m*x^m)/(1-x-x^m). Also 
               a(n) = 1 + n*sum(binomial(n-1-(m-1)*i, i-1)/i, i=1..n/m). This gives 
               the number of ways to cover (without overlapping) a ring lattice 
               (or necklace) of n sites with molecules that are m sites wide. Special 
               cases: m=2: A000204, m=3: A001609, m=4: A014097, m=5: A058368, m=6: 
               A058367, m=7: A058366, m=8: A058365, m=9: A058364.
%D A058366 E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional 
               lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
%D A058366 Y. Kong, General recurrence theory of ligand binding on a three-dimensional 
               lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.
%F A058366 a(n) = 1 + n*sum(binomial(n-1-6*i, i-1)/i, i=1..n/7). a(n) = a(n-1) + 
               a(n-7), a(n) = 1 for n = 1..6, a(7) = 8. generating function = (x+7*x^7)/
               (1-x-x^7).
%e A058366 a(7) = 8 because there is one way to put zero molecule to the necklace 
               and 7 ways to put one molecule.
%Y A058366 Cf. A000079, A003269, A003520, A005708, A005709, A005710.
%Y A058366 Sequence in context: A115842 A067682 A067729 this_sequence A120209 A138581 
               A097363
%Y A058366 Adjacent sequences: A058363 A058364 A058365 this_sequence A058367 A058368 
               A058369
%K A058366 nonn
%O A058366 1,7
%A A058366 Yong Kong (ykong(AT)curagen.com), Dec 17 2000