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Search: id:A105484
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| A105484 |
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Number of partitions of {1...n} containing 2 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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+0
6
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| 1, 2, 9, 38, 177, 882, 4711, 26795, 161583, 1028992, 6896067, 48487476, 356703531, 2738868784, 21901044795, 182022288438, 1569519971934, 14017732109520, 129480496353104, 1235228480628932, 12154988981496309, 123229919746398894
(list; graph; listen)
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OFFSET
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4,2
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REFERENCES
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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
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A. O. Munagi, Set Partitions with Successions and Separations,IJMMS 2005:3 (2005),451-463.
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FORMULA
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a(n)=Sum(c(n, k, 2), k=1...n), where c(n, k, 2) is the case r =2 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
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a(6)=9 because the partitions of {1,...,6} with 2 strings of 3 consecutive integers are 12346/5, 13456/2, 16/2345, 1234/56, 123/456, 12/3456, 1234/5/6, 1/2345/6, 1/2/3456.
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MAPLE
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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: A105484 := proc(n) local k ; add(c(n, k, 2), k=1..n) ; end: for n from 4 to 27 do printf("%d, ", A105484(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2007
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CROSSREFS
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Cf. A105483, A105485, A105488, A105492.
Sequence in context: A151003 A151004 A151005 this_sequence A151006 A151007 A151008
Adjacent sequences: A105481 A105482 A105483 this_sequence A105485 A105486 A105487
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KEYWORD
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nonn
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AUTHOR
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A. O. Munagi (amunagi(AT)yahoo.com), Apr 10 2005
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2007
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