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%I #5 Oct 03 2013 09:34:33
%S 1,6,36,210,1260,7833,50701,342126,2406645,17633820,134427468,
%T 1064801442,8751834839,74540800014
%N Number of partitions of {1,...,n} containing 2 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 A105484 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, 2), k=1...n), where w(n, k, 2) is the case r=2 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(7)=6; the enumerated partitions are 123567/4, 1237/456, 1567/234, 123/456/7, 123/4/567, 1/234/567.
%Y Cf. A105484, A105488, A105493.
%K more,nonn
%O 6,2
%A _Augustine O. Munagi_, Apr 11 2005