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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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, The Project Gutenberg EBook of Tintinnalogia, or, the Art of Ringing [From Alois P. Heinz, Aug 19 2008]

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-Fran├žois 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

AUTHOR

N. J. A. Sloane, Jan 24 2004

STATUS

approved

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Last modified October 25 20:31 EDT 2021. Contains 348256 sequences. (Running on oeis4.)