[seqfan] Re: A triangle I can't remember
Gottfried Helms
helms at uni-kassel.de
Tue Jul 4 19:58:32 CEST 2017
Am 04.07.2017 um 07:26 schrieb Peter Lawrence:
> Hugo,
> Wow, that’s impressive, but not the triangle I’m searching for.
> Still searching…
Perhaps this one?
Gottfried Helms
---------------------------------
>From - Tue Aug 07 09:19:26 2012
To: seqfan at list.seqfan.eu
Message-Id: <6D5E85C2-9BAD-43B2-9D06-D3598A8E7ECC at sbcglobal.net>
From: Peter Lawrence <peterl95124 at sbcglobal.net>
Date: Mon, 6 Aug 2012 21:03:57 -0700
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Subject: [seqfan] A178526 Fibonacci Triangle, and A001595
I stumbled[*] on an alternate definition for A178526 "Fibonacci
Triangle",
and for A001595.
using the naive recursion F(n) = F(n-1) + F(n-2), F(0) = 1, F(1) = 1,
T [r, c ] = number of times F(c) is evaluated when computing F(r)
for example the 4'th row is
1, 1, 2, 3, 2
indicating that F(4) is evaluated 1 times
F(3) 1
F(2) 2
F(1) 3
and F(0) 2
you can also get this from the "fibonacci tree" by simply counting
the number of occurrences of each number/label in the tree, without
the complication of giving weights to edges.
when you add up all the numbers in a row you get A001595,
which now can be interpreted as the total number of function calls
in evaluating the recursive Fibonacci formula.
Peter Lawrence.
[* by "stumbled" I mean I started with these definitions and found
that the sequences already existed !]
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