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 A105492 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. 2
 1, 6, 36, 210, 1260, 7833, 50701, 342126, 2406645, 17633820, 134427468, 1064801442, 8751834839, 74540800014 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 COMMENTS Partitions enumerated by A105484 in which the maximal length of consecutive integers in a block is 3. REFERENCES A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463 LINKS A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005), 451-463. FORMULA 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)). EXAMPLE a(7)=6; the enumerated partitions are 123567/4, 1237/456, 1567/234, 123/456/7, 123/4/567, 1/234/567. CROSSREFS Cf. A105484, A105488, A105493. Sequence in context: A096979 A269464 A123887 * A052748 A292297 A353344 Adjacent sequences:  A105489 A105490 A105491 * A105493 A105494 A105495 KEYWORD more,nonn AUTHOR Augustine O. Munagi, Apr 11 2005 STATUS approved

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