[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
X-Mailer: Apple Mail (2.753.1)
X-Content-Filtered-By: Mailman/MimeDel 2.1.15
Subject: [seqfan] A178526 Fibonacci Triangle, and A001595

I stumbled[*] on an alternate definition for A178526 "Fibonacci
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 !]


Seqfan Mailing list - http://list.seqfan.eu/

More information about the SeqFan mailing list