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A105485
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Number of partitions of {1...n} containing 3 strings of 3 consecutive integers, where each string is counted within a block and a string of more than 3 consecutive integers are counted three at a time.
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6
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1, 2, 10, 44, 215, 1112, 6141, 35968, 222659, 1451770, 9939702, 71265036, 533744979, 4166533826, 33831424388, 285213338300, 2492259168784, 22538314947452, 210639529104328, 2031804667766532, 20203377516199587
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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REFERENCES
| A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463.
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LINKS
| A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463.
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FORMULA
| a(n)=Sum(c(n, k, 3), k=1...n), where c(n, k, 3) is the case r=3 of c(n, k, r) given by c(n, k, r)=c(n-1, k-1, r)+(k-1)c(n-1, k, r)+c(n-2, k-1, r)+(k-1)c(n-2, k, r)+c(n-1, k, r-1)-c(n-2, k-1, r-1)-(k-1)c(n-2, k, r-1), r=0, 1, .., n-k-1, k=1, 2, .., n-2r, c(n, k, 0)=sum(binomial(n-j, j)*S2(n-j-1, k-1), j= 0..floor(n/2)).
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EXAMPLE
| a(6)=2 because the partitions of {1,...,6} with 3 strings of 3 consecutive integers are 12345/6, 1/23456.
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MAPLE
| c := proc(n, k, r) option remember ; local j ; if r =0 then add(binomial(n-j, j)*combinat[stirling2](n-j-1, k-1), j=0..floor(n/2)) ; else if r <0 or r > n-k-1 then RETURN(0) fi ; if n <1 then RETURN(0) fi ; if k <1 then RETURN(0) fi ; RETURN( c(n-1, k-1, r)+(k-1)*c(n-1, k, r)+c(n-2, k-1, r)+(k-1)*c(n-2, k, r) +c(n-1, k, r-1)-c(n-2, k-1, r-1)-(k-1)*c(n-2, k, r-1) ) ; fi ; end: A105485 := proc(n) local k ; add(c(n, k, 3), k=1..n) ; end: for n from 5 to 28 do printf("%d, ", A105485(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2007
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CROSSREFS
| Cf. A105482, A105484, A105489, A105493.
Sequence in context: A100397 A084059 A084609 * A151313 A144896 A142983
Adjacent sequences: A105482 A105483 A105484 * A105486 A105487 A105488
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KEYWORD
| nonn
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AUTHOR
| A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2007
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