%I A058365
%S A058365 1,1,1,1,1,1,1,9,10,11,12,13,14,15,16,25,35,46,58,71,85,100,116,141,
%T A058365 176,222,280,351,436,536,652,793,969,1191,1471,1822,2258,2794,3446,
%U A058365 4239,5208,6399,7870,9692,11950,14744,18190,22429,27637,34036,41906
%N A058365 Number of ways to cover (without overlapping) a ring lattice (necklace) 
               of n sites with molecules that are 8 sites wide.
%C A058365 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 A058365 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 A058365 Y. Kong, General recurrence theory of ligand binding on a three-dimensional 
               lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.
%F A058365 a(n) = 1 + n*sum(binomial(n-1-7*i, i-1)/i, i=1..n/8). a(n) = a(n-1) + 
               a(n-8), a(n) = 1 for n = 1..7, a(8) = 9. generating function = (x+8*x^8)/
               (1-x-x^8).
%e A058365 a(8) = 9 because there is one way to put zero molecule to the necklace 
               and 8 ways to put one molecule.
%Y A058365 Cf. A000079, A003269, A003520, A005708, A005709, A005710.
%Y A058365 Sequence in context: A023392 A060009 A115843 this_sequence A162789 A121816 
               A001731
%Y A058365 Adjacent sequences: A058362 A058363 A058364 this_sequence A058366 A058367 
               A058368
%K A058365 nonn
%O A058365 1,8
%A A058365 Yong Kong (ykong(AT)curagen.com), Dec 17 2000