6,1

Number of partitions enumerated by A105480 in which the maximal length of consecutive integers in a block is 2.

With offset 3t, number of partitions of {1...N} containing 3 detached strings of t consecutive integers, where N=n+3j, 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 three t-strings.

A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463.

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

a(n)=binomial(n-3, 3)*Bell(n-4), which is the case r=3 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).

a(6) = 2 because the partitions of {1,2,3,4,5,6} with 3 detached pairs of consecutive integers are 12/34/56, 1256/34.

seq(binomial(n-3, 3)*combinat[bell](n-4), n=6..25);

a:=n->sum(numbcomb (n, 2)*bell(n)/3, j=0..n): seq(a(n), n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

Cf. A105480, A105485, A105488, A105490.

Sequence in context: A081006 A000183 A081159 this_sequence A093302 A093130 A043029

Adjacent sequences: A105486 A105487 A105488 this_sequence A105490 A105491 A105492

easy,nonn

A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005