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 A143490 "Fourth down, Extream [sic] between the two farthest Bells from it" in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(1,2,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 3 in n-th permutation. 8
 3, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Start with (1,2,3,4), i.e. the first permutation of {1,2,3} followed by 4; then for each next permutation, transpose 4 one to the left; if at position 1, replace {1,2,3} recursively by the next permutation of these numbers. Thereafter, for each next permutation, transpose 4 to the right. And so on. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,-1,1). FORMULA Period 24. MAPLE ring:= proc(k::nonnegint) local p, i, left, l, nf, ini; if k<=1 then proc() [1\$k] end else ini := proc() p:= ring(k-1); i:= k; left:= true; l:= p(); nf:= k! end; ini(); proc() local ll; ll:= [seq(l[t], t=1..(i-1)), k, seq(l[t], t=i..(k-1))]; if left then if i>1 then i:= i-1 else left:= false; l:=p() fi else if i indx (bell(4)[modp(n-1, 24)+1], 3): seq (a(n), n=1..121); CROSSREFS Cf. A143484-A143490, A090281. Sequence in context: A014241 A199185 A262827 * A007485 A018244 A090589 Adjacent sequences:  A143487 A143488 A143489 * A143491 A143492 A143493 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Aug 19 2008 STATUS approved

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