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A105493
Number of partitions of {1,...,n} containing 3 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.
4
2, 20, 170, 1340, 10375, 80652, 636990, 5143740, 42613980, 362863600, 3178544754, 28650249848
OFFSET
9,1
COMMENTS
Partitions enumerated by A105485 in which the maximal length of consecutive integers in a block is 3.
REFERENCES
A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463
LINKS
FORMULA
a(n)=Sum(w(n, k, 3), k=1...n), where w(n, k, 3) is the case r=3 of w(n, k, r) given by w(m, k, r)=w(m-1, k-1, r)+(k-1)w(m-1, k, r)+w(m-2, k-1, r)+(k-1)w(m-2, k, r) +w(m-3, k-1, r-1)+(k-1)w(m-3, k, r-1) r=0, 1, ..., floor(n/3), k=1, 2, ..., n-2r, w(n, k, 0)=sum(binomial(n-j, j)*S2(n-j-1, k-1), j=0..floor(n/2)).
EXAMPLE
a(9)=2, the enumerated partitions are 123/789/456, 123/456/789.
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Augustine O. Munagi, Apr 11 2005
STATUS
approved