

A058365


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


8



1, 1, 1, 1, 1, 1, 1, 9, 10, 11, 12, 13, 14, 15, 16, 25, 35, 46, 58, 71, 85, 100, 116, 141, 176, 222, 280, 351, 436, 536, 652, 793, 969, 1191, 1471, 1822, 2258, 2794, 3446, 4239, 5208, 6399, 7870, 9692, 11950, 14744, 18190, 22429, 27637, 34036, 41906
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OFFSET

1,8


COMMENTS

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.


REFERENCES

E. Di Cera and Y. Kong, Theory of multivalent binding in one and twodimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107124.
Y. Kong, General recurrence theory of ligand binding on a threedimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 47904799.


LINKS

Table of n, a(n) for n=1..51.


FORMULA

a(n) = 1 + n*sum(binomial(n17*i, i1)/i, i=1..n/8). a(n) = a(n1) + a(n8), a(n) = 1 for n = 1..7, a(8) = 9. generating function = (x+8*x^8)/(1xx^8).


EXAMPLE

a(8) = 9 because there is one way to put zero molecule to the necklace and 8 ways to put one molecule.


CROSSREFS

Cf. A000079, A003269, A003520, A005708, A005709, A005710.
Sequence in context: A060009 A250042 A115843 * A162789 A121816 A196105
Adjacent sequences: A058362 A058363 A058364 * A058366 A058367 A058368


KEYWORD

nonn


AUTHOR

Yong Kong (ykong(AT)curagen.com), Dec 17 2000


STATUS

approved



