Search: id:A058368
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%I A058368
%S A058368 1,1,1,1,6,7,8,9,10,16,23,31,40,50,66,89,120,160,210,276,365,485,645,
%T A058368 855,1131,1496,1981,2626,3481,4612,6108,8089,10715,14196,18808,24916,
%U A058368 33005,43720,57916,76724,101640,134645,178365,236281,313005,414645
%N A058368 Number of ways to cover (without overlapping) a ring lattice (necklace) 
               of n sites with molecules that are 5 sites wide.
%C A058368 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 A058368 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 A058368 Y. Kong, General recurrence theory of ligand binding on a three-dimensional 
               lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.
%F A058368 a(n) = 1 + n*sum(binomial(n-1-4*i, i-1)/i, i=1..n/5). a(n) = a(n-1) + 
               a(n-5), a(n) = 1 for n = 1..4, a(5) = 6. generating function = (x+5*x^5)/
               (1-x-x^5).
%e A058368 a(5) = 6 because there is one way to put zero molecule to the necklace 
               and 5 ways to put one molecule.
%Y A058368 Cf. A000204, A001609, A014097, A000079, A003269, A003520, A005708, A005709, 
               A005710.
%Y A058368 Sequence in context: A069838 A067901 A115840 this_sequence A108613 A081408 
               A143616
%Y A058368 Adjacent sequences: A058365 A058366 A058367 this_sequence A058369 A058370 
               A058371
%K A058368 nonn
%O A058368 1,5
%A A058368 Yong Kong (ykong(AT)curagen.com), Dec 17 2000

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