A090281 "Plain Bob Minimus" in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), ... which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 1 (the treble bell) in n-th permutation.

1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3

Offset

1,2

Comments

This is the "plain hunting" sequence with 4 bells.

a(n) is also the position of bell 4 (the tenor bell) in the (n+4)-th permutation of the "Fourth down, Extream between the two farthest Bells from it" bell-ringing permutation, A143484. - Alois P. Heinz, Aug 19 2008

Period 8 sequence: 1, 2, 3, 4, 4, 3, 2, 1, ... - Wesley Ivan Hurt, Mar 27 2014

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

R. Bailey, Change Ringing Resources

David Joyner, Application: Bell Ringing

M.I.T. Bell-Ringers, General Information On Change Ringing

Richard Duckworth and Fabian Stedman, Tintinnalogia, or, the Art of Ringing, (1671). Released by Project Gutenberg, 2006.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).

Index entries for sequences related to bell ringing

Formula

a(n) = (floor(-abs(n-(16*ceiling(n/8)-7)/2) + (16*ceiling(n/8)-7)/2)) mod 8. - Wesley Ivan Hurt, Mar 26 2014

G.f.: -x*(x^4+x^3+x^2+x+1) / ((x-1)*(x^4+1)). - Colin Barker, Mar 26 2014

Example

The full list of the 24 permutations is as follows (the present sequence tells where the 1's are):
1 2 3 4
2 1 4 3
2 4 1 3
4 2 3 1
4 3 2 1
3 4 1 2
3 1 4 2
1 3 2 4
1 3 4 2
3 1 2 4
3 2 1 4
2 3 4 1
2 4 3 1
4 2 1 3
4 1 2 3
1 4 3 2
1 4 2 3
4 1 3 2
4 3 1 2
3 4 2 1
3 2 4 1
2 3 1 4
2 1 3 4
1 2 4 3

Maple

ring:= proc(k) option remember; local l, a, b, c, swap, h; l:= [1, 2, 3, 4]; swap:= proc(i, j) h:=l[i]; l[i]:=l[j]; l[j]:=h end; a:= proc() swap(1, 2); swap(3, 4); l[k] end; b:= proc() swap(2, 3); l[k] end; c:= proc() swap(3, 4); l[k] end; [l[k], seq([seq([a(), b()][], j=1..3), a(), c()][], i=1..3)] end: bells:=[seq(ring(k), k=1..4)]: indx:= proc(l, n, k) local i; for i from 1 to 4 do if l[i][n]=k then break fi od; i end: a:= n-> indx(bells, modp(n-1, 24)+1, 1): seq(a(n), n=1..99); # Alois P. Heinz, Aug 19 2008

Mathematica

Table[Mod[Floor[-Abs[n-(16*Ceiling[n/8]-7)/2] + (16*Ceiling[n/8]-7)/2], 8], {n, 100}] (* Wesley Ivan Hurt, Mar 26 2014 *)
LinearRecurrence[{1, 0, 0, -1, 1}, {1, 2, 3, 4, 4}, 105] (* Jean-François Alcover, Mar 15 2021 *)

Prog

(Scheme) (define (A090281 n) (list-ref '(1 2 3 4 4 3 2 1) (modulo (- n 1) 8))) ;; Antti Karttunen, Aug 10 2017

Crossrefs

Cf. A090277, A090278, A090279, A090280, A090282, A090283, A090284.

Sequence in context: A093150 A301297 A167831 * A316823 A051951 A262857

Adjacent sequences: A090278 A090279 A090280 * A090282 A090283 A090284

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 24 2004

Status

approved