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A334738
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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.
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1
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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
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0,2
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COMMENTS
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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".
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LINKS
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EXAMPLE
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0: 1: 2: 3: 4: 5:
-----------------------------------------------------------------------
x x-1 x-2 x-3 x-4 x-5
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|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
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||x-1|-2|
-----------------------
||x-1|-1| ||x-1|-1|-1
-----------------------------------------------------------
|x| |x|-1 |x|-2 |x|-3 |x|-4
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||x|-3|
-----------------------
||x|-2| ||x|-2|-1
-----------------------------------
||x|-1| ||x|-1|-1 ||x|-1|-2
-----------
|||x|-1|-1|
-----------------------------------------------------------------------
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PROG
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(Java) see link.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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