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Combinatorics

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  • Functions I understand in combinatorics

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  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
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  • EulerianCatalanNumber
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  • Fibbinary
  • FibonacciEncode
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PeterBurbery`Combinatorics`
Fibbinary
​
Fibbinary
[n]
gives the nth fibbinary number.
​
​
Fibbinary
[{n}]
gives a list of fibbinary numbers less than or equal to n.
​
Details and Options

Examples  
(4)
Basic Examples  
(3)
First one hundred fibbinaries:
In[1]:=
Table
Fibbinary
[n],{n,100}
Out[1]=
{1,2,4,5,8,9,10,16,17,18,20,21,32,33,34,36,37,40,41,42,64,65,66,68,69,72,73,74,80,81,82,84,85,128,129,130,132,133,136,137,138,144,145,146,148,149,160,161,162,164,165,168,169,170,256,257,258,260,261,264,265,266,272,273,274,276,277,288,289,290,292,293,296,297,298,320,321,322,324,325,328,329,330,336,337,338,340,341,512,513,514,516,517,520,521,522,528,529,530,532}
​
Fibbinaries less than or equal to 50, represented in base 2:
In[1]:=
BaseForm[#,2]&/@
Fibbinary
[{50}]//Column
Out[1]=
1
2
10
2
100
2
101
2
1000
2
1001
2
1010
2
10000
2
10001
2
10010
2
10100
2
10101
2
100000
2
100001
2
100010
2
100100
2
100101
2
101000
2
101001
2
101010
2
​
Plot of fibbinaries less than 150 in base 2:
In[1]:=
IntegerDigits
Fibbinary
[{150}],2//ArrayPlot
Out[1]=
Properties & Relations  
(1)

SeeAlso
ZeckendorfRepresentation
 
▪
FibonacciEncode
 
▪
InverseFibonacci
 
▪
Fibonacci
 
▪
IntegerPartitions
RelatedGuides
▪
Combinatorics
RelatedLinks
▪
Wikipedia—Fibbinary number
ZeckendorfRepresentation
▪
David Eppstein—Generating fibbinary numbers, three ways
Fibbinary
Resource Function created by Wolfram Staff, based on work by Jörg Arndt, Robert G. Wilson and Eric W. Weisstein
""

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