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Search: id:A067608
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| A067608 |
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Number of structural alkanes with combinatorial diameter n. |
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+0
4
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| 1, 1, 3, 6, 53, 496, 81096, 35292601, 211275732504203, 5013078952131335869356, 4188494841905497365271738826910705731652978, 13998172580873019733546655911268420464183123192214609601699428961
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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R. Davies and P. J. Freyd, C_{167}H_{336} is The Smallest Alkane with More Realizable Isomers than the Observable Universe has Particles, Journal of Chemical Education, Vol. 66, April 1989, pp. 278-281.
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EXAMPLE
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There are 53 such alkanes where the longest chain of carbon atoms is of length 5.
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MATHEMATICA
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rid[0]=1; rid[r_] := rid[r]=1+Binomial[rid[r-1]+2, 3]; rd[r_] := rid[r]-rid[r-1]; td[1]=1; td[r_] := If[EvenQ[r], Binomial[rd[r/2]+1, 2], Binomial[rid[(r-1)/2]+3, 4]-rd[(r-1)/2]Binomial[rid[(r-3)/2]+2, 3]-Binomial[rid[(r-3)/2]+3, 4]]; td/@Range[12]
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CROSSREFS
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Cf. A000602, A000628, A067609, A067610.
Sequence in context: A056447 A056437 A012275 this_sequence A023177 A132474 A032070
Adjacent sequences: A067605 A067606 A067607 this_sequence A067609 A067610 A067611
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KEYWORD
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nonn
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AUTHOR
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Peter Freyd (pjf(AT)saul.cis.upenn.edu), Feb 02 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Feb 11 2002
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