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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. 1
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..99.

R. Bailey, Change Ringing Resources

David Joyner, Application: Bell 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*(-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)

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(2)[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[2][[Mod[n-1, 24]+1]]; Table[a[n], {n, 1, 99}] (* Jean-Fran├žois Alcover, Mar 19 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A090277-A090284.

Sequence in context: A135941 A036998 A121464 * A256143 A274455 A153279

Adjacent sequences:  A090275 A090276 A090277 * A090279 A090280 A090281

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 24 2004

STATUS

approved

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Last modified September 22 08:23 EDT 2018. Contains 315270 sequences. (Running on oeis4.)