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 A090279 "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 3 of n-th permutation. 0
 3, 4, 1, 3, 2, 1, 4, 2, 4, 2, 1, 4, 3, 1, 2, 3, 2, 3, 1, 2, 4, 1, 3, 4, 3, 4, 1, 3, 2, 1, 4, 2, 4, 2, 1, 4, 3, 1, 2, 3, 2, 3, 1, 2, 4, 1, 3, 4, 3, 4, 1, 3, 2, 1, 4, 2, 4, 2, 1, 4, 3, 1, 2, 3, 2, 3, 1, 2, 4, 1, 3, 4, 3, 4, 1, 3, 2, 1, 4, 2, 4, 2, 1, 4, 3, 1, 2, 3, 2, 3, 1, 2, 4, 1, 3, 4, 3, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. Bailey, Change Ringing Resources David Joyner, Application: Bell Ringing Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1). FORMULA Period 24. From Chai Wah Wu, Jul 17 2016: (Start) a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) - a(n-14) + a(n-15) - a(n-16) + a(n-17) - a(n-18) + a(n-19) - a(n-20) + a(n-21) - a(n-22) + a(n-23) for n > 23. G.f.: x*(-4*x^22 + x^21 - 2*x^20 - 2*x^19 - x^17 - 2*x^16 - 3*x^14 + x^13 - 2*x^12 - x^11 - 3*x^10 + 2*x^9 - 4*x^8 - 2*x^6 - 2*x^5 + x^4 - 3*x^3 - x - 3)/((x - 1)*(x^2 + 1)*(x^4 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^8 - x^4 + 1)). (End) 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: a:= n-> ring(3)[modp(n-1, 24)+1]: seq(a(n), n=1..99); # Alois P. Heinz, Aug 19 2008 MATHEMATICA ring[k_] := ring[k] = Module[{l, a, b, c, swap, h}, l = Range[4]; 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]]}, Flatten @ Table[ Join[ Flatten @ Table[{a, b}, {j, 1, 3}], {a}, {c}], {i, 1, 3}]]]; a[n_] := ring[3][[Mod[n-1, 24]+1]]; Table[a[n], {n, 1, 99}] (* Jean-François Alcover, Mar 18 2017, after Alois P. Heinz *) CROSSREFS Cf. A090277-A090284. Sequence in context: A021297 A124909 A281098 * A101667 A117378 A278518 Adjacent sequences:  A090276 A090277 A090278 * A090280 A090281 A090282 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 24 2004 STATUS approved

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