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A143487
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"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 number in position 4 of n-th permutation.
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1
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4, 3, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 3, 3, 3, 4, 4, 3, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 3, 3, 3, 4, 4, 3, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 3, 3, 3, 4, 4, 3, 3, 3, 2, 2, 2, 4, 4, 2, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 3, 3, 3, 4, 4, 3, 3, 3, 2, 2, 2, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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LINKS
| The Project Gutenberg EBook of Tintinnalogia, or, the Art of Ringing, by Richard Duckworth and Fabian Stedman
Index entries for sequences related to bell ringing
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FORMULA
| Period 24.
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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<k then i:= i+1 else left:= true; l:=p() fi fi; nf:= nf-1; if nf = 0 then ini() fi; ll end fi end: bell := proc(k) option remember; local p; p:= ring(k); [seq(p(), i=1..k!)] end: a := n-> bell(4)[modp(n-1, 24)+1][4]: seq (a(n), n=1..121);
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CROSSREFS
| Cf. A143484-A143490, A090281.
Sequence in context: A016502 A117691 A171627 * A031350 A031353 A085415
Adjacent sequences: A143484 A143485 A143486 * A143488 A143489 A143490
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008
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