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 A058366 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 7 sites wide. 8

%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(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 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 Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.

%F 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 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

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Last modified February 22 14:45 EST 2020. Contains 332136 sequences. (Running on oeis4.)