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Search: id:A068330
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| A068330 |
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Consider all sublists of [(2,1),(3,2,1),(4,3,2,1),...,(n,...,4,3,2,1)] and multiply these permutations in that order. How many of the products are n-cycles? |
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1
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| 1, 1, 1, 2, 4, 6, 11, 20, 36, 65, 118, 215, 389, 727, 1366, 2565, 4849, 9123, 17168, 32629
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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If we take the inverse permutations to the above, or, equivalently, multiply them in the reverse order, we get another description of the sequences A000048 or A056303 with the first term omitted in each case.
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EXAMPLE
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a[5] (the output of the program below in which a is the list of the first n terms of the sequence) is 4 because that is the number of products of sublists of [(2,1),(3,2,1),(4,3,2,1),(5,4,3,2,1)] which are 5-cycles, namely (5,4,3,2,1) itself, (3,2,1)*(5,4,3,2,1)=(5,4,3,1,2), (2,1)*(4,3,2,1)*(5,4,3,2,1)=(5,4,2,3,1) and (2,1)*(3,2,1)*(4,3,2,1)*(5,4,3,2,1)=(5,4,2,1,3).
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PROGRAM
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(GAP) a := []; p := (); perms := [p]; for i in [1..n] do pp := perms*p; pp1 := Filtered(pp, m -> CycleLength(m, [1..i], 1) = i); a[i] := Length(pp1); perms := Union(perms, pp); p := p*(i, i+1); od;
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CROSSREFS
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Cf. A000048 A056303.
Sequence in context: A002097 A026757 A026385 this_sequence A017993 A049870 A093970
Adjacent sequences: A068327 A068328 A068329 this_sequence A068331 A068332 A068333
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KEYWORD
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nonn,nice
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AUTHOR
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Simon P. Norton (simon(AT)dpmms.cam.ac.uk), Feb 27 2002
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