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A090278 "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 number in position 2 of n-th permutation.

%I A090278 #20 Mar 18 2017 09:46:04
%S A090278 2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,
%T A090278 2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,
%U A090278 2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4
%N A090278 "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 number in position 2 of n-th permutation.
%H A090278 R. Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a>
%H A090278 David Joyner, <a href="http://www.usna.edu/Users/math/wdj/book/node158.html">Application: Bell Ringing</a>
%H A090278 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1).
%H A090278 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>
%F A090278 Period 24.
%F A090278 From _Chai Wah Wu_, Jul 17 2016: (Start)
%F A090278 a(n) = a(n-1) - a(n-6) + a(n-7) - a(n-12) + a(n-13) - a(n-18) + a(n-19) for n > 19.
%F A090278 G.f.: x*(-2*x^18 + x^17 - 2*x^16 + x^15 - 2*x^14 + x^13 - 2*x^11 - 2*x^10 + 4*x^9 - 3*x^8 - x^7 + x^6 - x^5 - x^4 + 2*x^3 - 3*x^2 + x - 2)/(x^19 - x^18 + x^13 - x^12 + x^7 - x^6 + x - 1). (End)
%p A090278 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: a:= n-> ring(2)[modp(n-1, 24)+1]: seq (a(n), n=1..99); # _Alois P. Heinz_, Aug 19 2008
%t A090278 ring[k_] := ring[k] = Module[{l = Range[4], a, b, c, swap, h}, swap[i_, j_] := (h = l[[i]]; l[[i]] = l[[j]]; l[[j]] = h); a := (swap[1, 2]; swap[3, 4]; l[[k]]); b := (swap[2, 3]; l[[k]]); c := (swap[3, 4]; l[[k]]); Join[{l[[k]]}, Table[{Table[{a, b}, {j, 1, 3}], a, c}, {i, 1, 3}]] // Flatten]; a[n_] := ring[2][[Mod[n-1, 24]+1]]; Table[a[n], {n, 1, 99}] (* _Jean-François Alcover_, Mar 19 2014, after _Alois P. Heinz_ *)
%Y A090278 Cf. A090277-A090284.
%K A090278 nonn
%O A090278 1,1
%A A090278 _N. J. A. Sloane_, Jan 24 2004