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A060112
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Sums of nonconsecutive factorial numbers.
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6
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0, 1, 2, 6, 7, 24, 25, 26, 120, 121, 122, 126, 127, 720, 721, 722, 726, 727, 744, 745, 746, 5040, 5041, 5042, 5046, 5047, 5064, 5065, 5066, 5160, 5161, 5162, 5166, 5167, 40320, 40321, 40322, 40326, 40327, 40344, 40345, 40346, 40440, 40441, 40442
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Zeckendorf (Fibonacci) expansion of n (A003714) reinterpreted as a factorial expansion.
Also positions in A055089, A060117 and A060118 of the permutations that are composed of disjoint adjacent transpositions only. (That these positions are same can be seen by comparing algorithms PermRevLexUnrankAMSD, PermUnrank3R, PermUnrank3L in the respective sequences). Thus also positions of the fixed terms in A065181 - A065184. See comment at A065163.
Written as disjoint cycles the permutations are: (), (1 2), (2 3), (3 4), (1 2)(3 4), (4 5), (1 2)(4 5), (2 3)(4 5), etc. Apart from the first one (the identity), these are the only kind of permutations used in campanology when moving from one "change" to next.
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REFERENCES
| Arthur T. White: Ringing the Changes, Math. Proc. Camb. Phil. Soc., September 1983, Vol. 94, part 2, pp. 203-215
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LINKS
| Index entries for sequences related to bell ringing
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FORMULA
| a(n) = PermRevLexRank(CampanoPerm(n))
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EXAMPLE
| Zeckendorf Expansions of first few natural numbers and the corresponding values when interpreted as factorial expansions: 0 = 0 = 0, 1 = 1 = 1, 2 = 10 = 2, 3 = 100 = 6, 4 = 101 = 7, 5 = 1000 = 24, 6 = 1001 = 25, 7 = 1010 = 26, 8 = 10000 = 120, etc.,
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MAPLE
| CampanoPerm := proc(n) local z, p, i; p := []; z := fibbinary(n); i := 1; while(z > 0) do if(1 = (z mod 2)) then p := permul(p, [[i, i+1]]); fi; i := i+1; z := floor(z/2); od; RETURN(convert(p, 'permlist', i)); end;
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CROSSREFS
| Subset of A059590. Cf. also A064640.
For PermRevLexRank, see A056019, for fibbinary see A048679 and A003714.
Sequence in context: A095036 A100901 A004791 * A057914 A057249 A155003
Adjacent sequences: A060109 A060110 A060111 * A060113 A060114 A060115
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Antti Karttunen, Mar 01 2001
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