%I A060112
%S A060112 0,1,2,6,7,24,25,26,120,121,122,126,127,720,721,722,726,727,744,745,
%T A060112 746,5040,5041,5042,5046,5047,5064,5065,5066,5160,5161,5162,5166,5167,
%U A060112 40320,40321,40322,40326,40327,40344,40345,40346,40440,40441,40442
%N A060112 Sums of nonconsecutive factorial numbers.
%C A060112 Zeckendorf (Fibonacci) expansion of n (A003714) reinterpreted as a factorial 
               expansion.
%C A060112 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.
%C A060112 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.
%D A060112 Arthur T. White: Ringing the Changes, Math. Proc. Camb. Phil. Soc., September 
               1983, Vol. 94, part 2, pp. 203-215
%H A060112 <a href="Sindx_Be.html#bell_ringing">Index entries for sequences related 
               to bell ringing</a>
%F A060112 a(n) = PermRevLexRank(CampanoPerm(n))
%e A060112 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.,
%p A060112 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;
%Y A060112 Subset of A059590. Cf. also A064640.
%Y A060112 For PermRevLexRank, see A056019, for fibbinary see A048679 and A003714.
%Y A060112 Sequence in context: A095036 A100901 A004791 this_sequence A057914 A057249 
               A155003
%Y A060112 Adjacent sequences: A060109 A060110 A060111 this_sequence A060113 A060114 
               A060115
%K A060112 nonn,easy,nice
%O A060112 0,3
%A A060112 Antti Karttunen, Mar 01 2001