|
Search: id:A058365
|
|
|
| A058365 |
|
Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 8 sites wide. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,8
|
|
|
COMMENT
|
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.
|
|
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.
Adjacent sequences: A058362 A058363 A058364 this_sequence A058366 A058367 A058368
Sequence in context: A023392 A060009 A115843 this_sequence A121816 A001731 A129849
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Yong Kong (ykong(AT)curagen.com), Dec 17 2000
|
|
|
Search completed in 0.002 seconds
|
