[seqfan] Re: Decimal expansions related to Metallic Means, and Pascal Triangle

Jess Tauber yahganlang at gmail.com
Fri Aug 23 04:37:07 CEST 2013


Well, I've started working out the rules for the decimal expansions of
straight-line relations for other generalized Pascal Triangles. The (2,1)
sided Triangle (which sums to Fib on the 1's side, upwards, and to Luc on
the other, again upwards along shallow diagonals) has decimalizations which
are sums of those from the classical Triangle, but the sums are themselves
distributed over negative powers of 10. My guess will be that all these
other Triangles are rule based and derived from the classical (1,1) sided
Pascal system, which makes sense since their generalized Fib sequences are.
Now I only wish I could figure out how to reverse-engineer some
Pascal-style system for dealing with Pell and other sequences related to
the other Metallic Means so I could explore THEIR guts.


On Wed, Aug 21, 2013 at 1:53 PM, Jess Tauber <yahganlang at gmail.com> wrote:

>
>
>
> Thanks. But let's backtrack a bit. I can analyze these things the hard
> way, by playing around with basic  operations with a calculator and an
> extended copy of the Pascal Triangle, but I'm no way even basically trained
> to be able to do this stuff in any kind of efficient way. I don't even know
> the correct nomenclatural or formulaic conventions unless I accidentally
> stumble upon them online. So what are good primers for someone in my
> situation?
>
> Jess Tauber
>



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