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 A090277 "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 1 of n-th permutation. 7
 1, 2, 2, 4, 4, 3, 3, 1, 1, 3, 3, 2, 2, 4, 4, 1, 1, 4, 4, 3, 3, 2, 2, 1, 1, 2, 2, 4, 4, 3, 3, 1, 1, 3, 3, 2, 2, 4, 4, 1, 1, 4, 4, 3, 3, 2, 2, 1, 1, 2, 2, 4, 4, 3, 3, 1, 1, 3, 3, 2, 2, 4, 4, 1, 1, 4, 4, 3, 3, 2, 2, 1, 1, 2, 2, 4, 4, 3, 3, 1, 1, 3, 3, 2, 2, 4, 4, 1, 1, 4, 4, 3, 3, 2, 2, 1, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..99. R. Bailey, Change Ringing Resources David Joyner, Application: Bell Ringing M.I.T. Bell-Ringers, General Information On Change Ringing Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1). Index entries for sequences related to bell ringing FORMULA Period 24. From Chai Wah Wu, Jul 17 2016: (Start) 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. G.f.: x*(-x^18 - x^17 - x^15 - x^13 - x^12 + 2*x^11 - 4*x^9 + x^7 - x^6 + x^5 - 2*x^3 - x - 1)/(x^19 - x^18 + x^13 - x^12 + x^7 - x^6 + x - 1). (End) EXAMPLE The full list of the 24 permutations is as follows (the present sequence gives the first column): 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: a:= n-> ring(1)[modp(n-1, 24)+1]: seq (a(n), n=1..99); # Alois P. Heinz, Aug 19 2008 MATHEMATICA 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[1][[Mod[n-1, 24]+1]]; Table[a[n], {n, 1, 99}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *) CROSSREFS Cf. A090278-A090284. Sequence in context: A339179 A182923 A263856 * A324662 A024222 A196063 Adjacent sequences: A090274 A090275 A090276 * A090278 A090279 A090280 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 24 2004 STATUS approved

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Last modified June 16 05:10 EDT 2024. Contains 373423 sequences. (Running on oeis4.)