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%I #45 Oct 13 2022 12:30:25
%S 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,
%T 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,
%U 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
%N "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.
%C This is the "plain hunting" sequence with 4 bells.
%C 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
%C Period 8 sequence: 1, 2, 3, 4, 4, 3, 2, 1, ... - _Wesley Ivan Hurt_, Mar 27 2014
%H Antti Karttunen, <a href="/A090281/b090281.txt">Table of n, a(n) for n = 1..8192</a>
%H R. Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H David Joyner, <a href="http://www.usna.edu/Users/math/wdj/book/node158.html">Application: Bell Ringing</a>
%H M.I.T. Bell-Ringers, <a href="http://web.mit.edu/bellringers/www/html/change_instruction.html">General Information On Change Ringing</a>
%H Richard Duckworth and Fabian Stedman, <a href="http://www.gutenberg.org/files/18567/18567-h/18567-h.htm">Tintinnalogia, or, the Art of Ringing</a>, (1671). Released by Project Gutenberg, 2006.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1,1).
%H <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>
%F 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
%F G.f.: -x*(x^4+x^3+x^2+x+1) / ((x-1)*(x^4+1)). - _Colin Barker_, Mar 26 2014
%e The full list of the 24 permutations is as follows (the present sequence tells where the 1's are):
%e 1 2 3 4
%e 2 1 4 3
%e 2 4 1 3
%e 4 2 3 1
%e 4 3 2 1
%e 3 4 1 2
%e 3 1 4 2
%e 1 3 2 4
%e 1 3 4 2
%e 3 1 2 4
%e 3 2 1 4
%e 2 3 4 1
%e 2 4 3 1
%e 4 2 1 3
%e 4 1 2 3
%e 1 4 3 2
%e 1 4 2 3
%e 4 1 3 2
%e 4 3 1 2
%e 3 4 2 1
%e 3 2 4 1
%e 2 3 1 4
%e 2 1 3 4
%e 1 2 4 3
%p 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
%t 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 *)
%t LinearRecurrence[{1, 0, 0, -1, 1}, {1, 2, 3, 4, 4}, 105] (* _Jean-François Alcover_, Mar 15 2021 *)
%o (Scheme) (define (A090281 n) (list-ref '(1 2 3 4 4 3 2 1) (modulo (- n 1) 8))) ;; _Antti Karttunen_, Aug 10 2017
%Y Cf. A090277, A090278, A090279, A090280, A090282, A090283, A090284.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jan 24 2004
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