[seqfan] Re: Golay-Rudin-Shapiro sequences
Kevin Ryde
user42 at zip.com.au
Tue Jun 12 04:06:15 CEST 2012
njasloane at gmail.com (Neil Sloane) writes:
>
> I have been cleaning up a bunch of sequences related to the
> Golay-Rudin-Shapiro (aka Rudin-Shapiro) sequence (or word).
> The main sequence is A020985.
I was tinkering recently with the connection of those to the alternate
paper folding curve A106665. I think that may be well-known, but my
cribs as follows if it might inspire cross references.
A020985 -- Golay/Rudin/Shapiro sequence
dX and dY, skipping every second value zero
dSum, change in X+Y
dX = GRS(N) if N even
0 if N odd
dY = 0 if N even
GRS(N) if N odd
dSum = dX + dY = GRS(N)
A020986 -- Golay/Rudin/Shapiro cumulative
X coordinate undoubled
A020990 -- Golay/Rudin/Shapiro * (-1)^n, cumulative
Y coordinate undoubled
X-Y diff, starting from N=1
I take the curve as first step along the X axis to X=1,Y=0 and then
upwards to X=1,Y=1, etc. By "undoubled" I mean the X coordinate doubles
up as 0 then 1,1,2,2,etc and A020986 is every second such value. Is the
jargon "bisection"? I suppose it's X=A020986(ceil(n/2)) or something
like that, starting from n=0.
Bit more notes I made under "dX,dY" code at
http://search.cpan.org/perldoc?Math::PlanePath::AlternatePaper#dX%2CdY
but I worry it's not reading very clearly yet :-)
--
Even the white bits were black.
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