OFFSET
1,2
LINKS
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).
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 24 2004
STATUS
approved