1,4

Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 4 sites wide.

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.

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. J. Broadhurst, Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams

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

Cf. A020999.

Cf. also A000204, A001609, A000079, A003269, A003520, A005708, A005709, A005710.

Adjacent sequences: A014094 A014095 A014096 this_sequence A014098 A014099 A014100

Sequence in context: A047322 A080703 A047575 this_sequence A081407 A066263 A089192

nonn

David Broadhurst (D.Broadhurst(AT)open.ac.uk)

Additional comments from Yong Kong (ykong(AT)curagen.com), Dec 16 2000