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A105491 Number of partitions of {1...n} containing 5 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly five 2-strings. 3
15, 312, 4263, 49112, 521640, 5329044, 53580450, 537427440, 5422899339, 55344162874, 573270663966, 6040762924560, 64851119605636, 709986204480672, 7931189102016852, 90430835147203728, 1052534895931584828 (list; graph; refs; listen; history; text; internal format)



Number of partitions enumerated by A105482 in which the maximal length of consecutive integers in a block is 2.

With offset 5t, number of partitions of {1,...,N} containing 5 detached strings of t consecutive integers, where N=n+5j, 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 five t-strings.


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


Table of n, a(n) for n=10..26.

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


a(n)=binomial(n-5, 5)*Bell(n-6), which is the case r=5 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(10)=15; the enumerated 15 partitions of {1,...,10} with 5 detached pairs of consecutive integers include (1,2,5,6,9,10)(3,4,7,8) and (1,2,9,10)(3,4,7,8)(5,6).


seq(binomial(n-5, 5)*combinat[bell](n-6), n=10..30);


Cf. A105482, A105490, A105487.

Sequence in context: A051691 A247238 A135390 * A158533 A284070 A133766

Adjacent sequences:  A105488 A105489 A105490 * A105492 A105493 A105494




Augustine O. Munagi, Apr 10 2005



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Last modified December 2 10:40 EST 2021. Contains 349437 sequences. (Running on oeis4.)