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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

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.

REFERENCES

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.

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

LINKS

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

FORMULA

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).

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

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.