8,1

Number of partitions enumerated by A105481 in which the maximal length of consecutive integers in a block is 2.

With offset 4t, number of partitions of {1...N} containing 4 detached strings of t consecutive integers, where N=n+4j, 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 four 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-4, 4)*Bell(n-5), which is the case r=4 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(8) = 5 because the partitions of {1,...,8} with 4 detached pairs of consecutive integers are 1256/3478, 1256/34/78, 12/3478/56, 1278/34/56, 12/34/56/78.

seq(binomial(n-4, 4)*combinat[bell](n-5), n=8..28);

a:=n->sum(numbcomb(n, 3)*bell(n)/4, j=0..n): seq(a(n), n=3..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

Cf. A105481, A105489, A105491, A105486.

Sequence in context: A151752 A127212 A091903 this_sequence A105494 A030986 A091882

Adjacent sequences: A105487 A105488 A105489 this_sequence A105491 A105492 A105493

easy,nonn

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