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%I #6 Oct 03 2013 09:34:33
%S 2,20,170,1340,10375,80652,636990,5143740,42613980,362863600,
%T 3178544754,28650249848
%N 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.
%C Partitions enumerated by A105485 in which the maximal length of consecutive integers in a block is 3.
%D A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463
%H A. O. Munagi, <a href="http://www.emis.de/journals/HOA/IJMMS/2005/3451.pdf">Set Partitions with Successions and Separations</a>,IJMMS 2005:3 (2005), 451-463.
%F 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)).
%e a(9)=2, the enumerated partitions are 123/789/456, 123/456/789.
%Y Cf. A105485, A105489, A105492.
%K more,nonn
%O 9,1
%A _Augustine O. Munagi_, Apr 11 2005
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