A334738 - OEIS

A334738

Iterate function composition by applying y=abs(x) or y=x-1. a(n) is the number of functions at distance n from the identity (y=x) in the graph of all possible results.

1, 2, 3, 5, 8, 13, 21, 33, 52, 81, 126, 194, 296, 451, 682, 1031, 1548, 2314, 3453, 5125, 7593, 11212, 16508, 24250, 35525, 51931, 75734, 110239, 160135, 232178, 336041, 485529, 700401, 1008750, 1450770, 2083412

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OFFSET

0,2

COMMENTS

The first 7 terms of this sequence are Fibonacci numbers. There indeed is an imperfect analogy with the rabbit problem: view applying y=x-1 as aging 1 month and applying y=abs(x) as [having a good chance of] procreating/being born; then the fact that the nodes of the abs(something) form do not generate new nodes when y=abs(x) is applied to them can be viewed as first month's immaturity. The reason why this sequence deviates from Fibonacci's is the existence of identities such as abs(abs(abs(abs(x)-1)-1)-1) = abs(abs(abs(x)-2)-1), and this precise example proves that abs(abs(abs(x)-1)-1)-1, "although aged >=1, is immature".

LINKS

Table of n, a(n) for n=0..35.

Luc Rousseau, A Java program that computes A334738.

EXAMPLE

0: 1: 2: 3: 4: 5:

-----------------------------------------------------------------------

x x-1 x-2 x-3 x-4 x-5

-----------

|x-4|

-----------------------

|x-3| |x-3|-1

-----------------------------------

|x-2| |x-2|-1 |x-2|-2

-----------

||x-2|-1|

-----------------------------------------------

|x-1| |x-1|-1 |x-1|-2 |x-1|-3

-----------

||x-1|-2|

-----------------------

||x-1|-1| ||x-1|-1|-1

-----------------------------------------------------------

|x| |x|-1 |x|-2 |x|-3 |x|-4

-----------

||x|-3|

-----------------------

||x|-2| ||x|-2|-1

-----------------------------------

||x|-1| ||x|-1|-1 ||x|-1|-2

-----------

|||x|-1|-1|

-----------------------------------------------------------------------

PROG

(Java) see link.

CROSSREFS

Cf. A000045.

Sequence in context: A240733 A283936 A278800 * A286938 A055806 A358902

Adjacent sequences: A334735 A334736 A334737 * A334739 A334740 A334741

KEYWORD

nonn,more

AUTHOR

Luc Rousseau, May 09 2020

STATUS

approved