1,4

Start with (1,2,3,4), i.e. the first permutation of {1,2,3} followed by 4; then for each next permutation, transpose 4 one to the left; if at position 1, replace {1,2,3} recursively by the next permutation of these numbers. Thereafter, for each next permutation, transpose 4 to the right. And so on.

The Project Gutenberg EBook of Tintinnalogia, or, the Art of Ringing, by Richard Duckworth and Fabian Stedman

Index entries for sequences related to bell ringing

Period 24.

The full list of the 24 permutations is as follows (the present sequence gives position of bell 1):

1 2 3 4

1 2 4 3

1 4 2 3

4 1 2 3

4 1 3 2

1 4 3 2

1 3 4 2

1 3 2 4

3 1 2 4

3 1 4 2

3 4 1 2

4 3 1 2

4 3 2 1

3 4 2 1

3 2 4 1

3 2 1 4

2 3 1 4

2 3 4 1

2 4 3 1

4 2 3 1

4 2 1 3

2 4 1 3

2 1 4 3

2 1 3 4

ring:= proc(k::nonnegint) local p, i, left, l, nf, ini; if k<=1 then proc() [1$k] end else ini := proc() p:= ring(k-1); i:= k; left:= true; l:= p(); nf:= k! end; ini(); proc() local ll; ll:= [seq(l[t], t=1..(i-1)), k, seq(l[t], t=i..(k-1))]; if left then if i>1 then i:= i-1 else left:= false; l:=p() fi else if i<k then i:= i+1 else left:= true; l:=p() fi fi; nf:= nf-1; if nf = 0 then ini() fi; ll end fi end: bell := proc(k) option remember; local p; p:= ring(k); [seq(p(), i=1..k!)] end: indx:= proc(l, k) local i; for i from 1 to nops(l) do if l[i]=k then break fi od; i end: a := n-> indx (bell(4)[modp(n-1, 24)+1], 1): seq (a(n), n=1..121);

Cf. A143484-A143490, A090281.

Sequence in context: A025451 A006513 A105224 this_sequence A047070 A071127 A029381

Adjacent sequences: A143485 A143486 A143487 this_sequence A143489 A143490 A143491

nonn

Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008