A105494 Number of partitions of {1,...,n} containing 4 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.

5, 75, 855, 8665, 83485, 788515, 7424515, 70378930, 675685240, 6594991405, 65598204272

Offset

12,1

Comments

Partitions enumerated by A105486 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

Table of n, a(n) for n=12..22.

A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005), 451-463.

Formula

a(n)=Sum(w(n, k, 4), k=1...n), where w(n, k, 4) is the case r=4 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(12)=5, the enumerated partitions are (1,2,3,7,8,9)(4,5,6,10,11,12),
(1,2,3,7,8,9)(4,5,6)(10,11,12), (1,2,3)(4,5,6,10,11,12)(7,8,9),
(1,2,3,10,11,12)(4,5,6)(7,8,9), (1,2,3)(4,5,6)(7,8,9) (10,11,12).

Crossrefs

Cf. A105486, A105490, A105493.

Sequence in context: A091903 A105490 A307823 * A030986 A284924 A248340

Adjacent sequences: A105491 A105492 A105493 * A105495 A105496 A105497

Keyword

more,nonn

Author

Augustine O. Munagi, Apr 11 2005

Status

approved