[seqfan] Re: the revolver sequence

[Tanya Khovanova]

This is my list for n=9:

{{0, 0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 1, 1, 1}, {0, 0, 0, 
  0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 1, 0, 1, 1, 1}, {0, 0, 0, 0, 1, 1, 
  0, 1, 1}, {0, 0, 0, 0, 1, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 1, 1, 
  1}, {0, 0, 0, 1, 1, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1, 0, 0, 1}, {0, 0,
   0, 0, 1, 1, 1, 1, 1}, {0, 0, 0, 1, 0, 1, 1, 1, 1}, {0, 0, 0, 1, 1, 
  0, 1, 1, 1}, {0, 0, 0, 1, 1, 1, 0, 1, 1}, {0, 0, 0, 1, 1, 1, 1, 0, 
  1}, {0, 0, 1, 0, 0, 1, 1, 1, 1}, {0, 0, 1, 1, 0, 0, 1, 1, 1}, {0, 0,
   0, 1, 1, 1, 1, 1, 1}, {0, 0, 1, 1, 1, 1, 1, 1, 1}}

--- On Wed, 9/23/09, Max Alekseyev <maxale at gmail.com> wrote:

> From: Max Alekseyev <maxale at gmail.com>
> Subject: [seqfan] Re: the revolver sequence
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Wednesday, September 23, 2009, 6:58 PM
> Hi Tanya,
> 
> I've got different values starting with a(9) = 13, a(10) =
> 32 etc.
> Could you please double check your values or lists all 18
> ways of
> loading a revolver with n=9 chambers?
> 
> Thanks,
> Max
> 
> On Wed, Sep 23, 2009 at 5:06 PM, Tanya Khovanova
> <mathoflove-seqfan at yahoo.com>
> wrote:
> > Hello all,
> >
> > I just submitted a sequence related to the revolver
> puzzle:
> > http://blog.tanyakhovanova.com/?p=174
> >
> > I generalized it to revolvers having n chambers.
> >
> > I think there should be more sequences: for example,
> the one when it is preferable to spin and the one when the
> chances are the same.
> >
> > Also, my programs are usually not very efficient. It
> will be nice if someone can add more terms to this
> sequence.
> >
> > %I A165646
> > %S A165646 0,0,0,0,2,3,4,5,18,43,60,84,294,472,724
> > %N A165646 The revolver sequence.
> > %C A165646 a(n) is in how many ways you can load a
> revolver with n chambers, so that if a person survives after
> the first shot, he/she has better chances of survival for
> the second shot if the shooter continues rather than spins.
> a(n) <= A000031(n) as A000031(n) counts the number of
> possible revolver loadings.
> > %H A165646 Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=174">Heard on the
> Street</a>
> > %e A165646 Based on the famous interview question
> where the revolver has six chambers and the shooter loads
> two adjacent bullets. As the answer to this question is to
> continue, a(6) must be at least 1.
> > %t A165646 << Combinatorica` colors[x_] :=
> Table[PadLeft[Table[1, {n, i}], x], {i, 0, x}]
> continueBetter[list_] := (len = Length[list]; c0 = 0; c00 =
> 0; rotateN = 0; While[rotateN < len, newList =
> RotateLeft[list, rotateN]; If[newList[[1]] == 0, c0++;
> If[newList[[2]] == 0, c00++]]; rotateN++]; If[c0 > 0,
> c00/c0 > c0/len, False]) continueNum[num_] := (neckNum =
> Length[colors[num]]; ans = 0; count = 1; While[count <=
> neckNum, ans = ans + Length[Select[ListNecklaces[num,
> colors[num][[count]], Cyclic], continueBetter[#] &]];
> count++]; ans) Table[continueNum[n], {n, 2, 15}]
> > %Y A165646 A000031
> > %K A165646 more,nonn
> > %O A165646 1,5
> > %A A165646 Tanya Khovanova (tanyakh(AT)yahoo.com), Sep
> 23 2009
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> 
> 
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