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.

2, 20, 170, 1340, 10375, 80652, 636990, 5143740, 42613980, 362863600, 3178544754, 28650249848

Offset: 9

Author

Augustine O. Munagi, Apr 11 2005

Keywords

• more
• nonn

Comments

Partitions enumerated by A105485 in which the maximal length of consecutive integers in a block is 3.

Examples

			a(9)=2, the enumerated partitions are 123/789/456, 123/456/789.
		

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.

Crossrefs

Cf. A105485, A105489, A105492.

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)).