OFFSET
10,1
COMMENTS
Number of partitions enumerated by A105482 in which the maximal length of consecutive integers in a block is 2.
With offset 5t, number of partitions of {1,...,N} containing 5 detached strings of t consecutive integers, where N=n+5j, t=2+j, j = 0,1,2,..., i.e., partitions of {1,...,N} in which only v-strings of consecutive integers can appear in a block, where v=1 or v=t and there are exactly five t-strings.
REFERENCES
A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463.
LINKS
A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463.
FORMULA
a(n)=binomial(n-5, 5)*Bell(n-6), which is the case r=5 in the general case of r pairs, d(n, r)=binomial(n-r, r)*Bell(n-r-1), which is the case t=2 of the general formula d(n, r, t)=binomial(n-r*(t-1), r)*B(n-r*(t-1)-1).
EXAMPLE
a(10)=15; the enumerated 15 partitions of {1,...,10} with 5 detached pairs of consecutive integers include (1,2,5,6,9,10)(3,4,7,8) and (1,2,9,10)(3,4,7,8)(5,6).
MAPLE
seq(binomial(n-5, 5)*combinat[bell](n-6), n=10..30);
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Augustine O. Munagi, Apr 10 2005
STATUS
approved