%I
%S 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 301,378,469,582,726,911,1148,1449,1827,2296,2878,3604,4515,5663,7112,
%U 8939,11235,14113,17717,22232,27895,35007,43946,55181,69294,87011
%N Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 7 sites wide.
%C This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n1) + a(nm), with a(n) = 1 for n = 1...m1, a(m) = m+1. The generating function is (x+m*x^m)/(1xx^m). Also a(n) = 1 + n*sum(binomial(n1(m1)*i, i1)/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 E. Di Cera and Y. Kong, Theory of multivalent binding in one and twodimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107124.
%D Y. Kong, General recurrence theory of ligand binding on a threedimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 47904799.
%F a(n) = 1 + n*sum(binomial(n16*i, i1)/i, i=1..n/7). a(n) = a(n1) + a(n7), a(n) = 1 for n = 1..6, a(7) = 8. generating function = (x+7*x^7)/(1xx^7).
%e a(7) = 8 because there is one way to put zero molecule to the necklace and 7 ways to put one molecule.
%Y Cf. A000079, A003269, A003520, A005708, A005709, A005710.
%K nonn
%O 1,7
%A Yong Kong (ykong(AT)curagen.com), Dec 17 2000
