

A060112


Sums of nonconsecutive factorial numbers.


12



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
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OFFSET

0,3


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.


REFERENCES

Arthur T. White: Ringing the Changes, Math. Proc. Camb. Phil. Soc., September 1983, Vol. 94, part 2, pp. 203215


LINKS

Table of n, a(n) for n=0..44.
Index entries for sequences related to bell ringing


FORMULA

a(n) = PermRevLexRank(CampanoPerm(n))


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.,


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;


CROSSREFS

Subset of A059590. Cf. also A064640.
For PermRevLexRank, see A056019, for fibbinary see A048679 and A003714.
Sequence in context: A004791 A220946 A243795 * A057914 A216037 A250547
Adjacent sequences: A060109 A060110 A060111 * A060113 A060114 A060115


KEYWORD

nonn,easy,nice


AUTHOR

Antti Karttunen, Mar 01 2001


STATUS

approved



