%I A014097
%S A014097 1,1,1,5,6,7,8,13,19,26,34,47,66,92,126,173,239,331,457,
%T A014097 630,869,1200,1657,2287,3156,4356,6013,8300,11456,15812,
%U A014097 21825,30125,41581,57393,79218,109343,150924,208317,287535
%N A014097 a(n)=a(n-1)+a(n-4).
%C A014097 Number of ways to cover (without overlapping) a ring lattice (necklace) 
               of n sites with molecules that are 4 sites wide.
%C A014097 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 A014097 E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional 
               lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
%H A014097 D. J. Broadhurst, <a href="http://arXiv.org/abs/hep-th/9612012">Conjectured 
               enumeration of irreducible multiple zeta values, from knots and Feynman 
               diagrams</a>
%F A014097 G.f.: -x*(1+4*x^3)/(-1+x+x^4). a(n)= 4*A003269(n)-3*A003269(n-1). - R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
%Y A014097 Cf. A020999.
%Y A014097 Cf. also A000204, A001609, A000079, A003269, A003520, A005708, A005709, 
               A005710.
%Y A014097 Sequence in context: A047322 A080703 A047575 this_sequence A081407 A066263 
               A089192
%Y A014097 Adjacent sequences: A014094 A014095 A014096 this_sequence A014098 A014099 
               A014100
%K A014097 nonn
%O A014097 1,4
%A A014097 David Broadhurst (D.Broadhurst(AT)open.ac.uk)
%E A014097 Additional comments from Yong Kong (ykong(AT)curagen.com), Dec 16 2000