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A228603
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a(1) = 9, a(2) = 44, a(n) = 4*(a(n-1) + a(n-2)) (n >=3).
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0
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9, 44, 212, 1024, 4944, 23872, 115264, 556544, 2687232, 12975104, 62649344, 302497792, 1460588544, 7052345344, 34051735552, 164416323584, 793872236544, 3833154240512, 18508105908224, 89365040594944, 431492586012672, 2083430506430464, 10059692369772544
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OFFSET
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1,1
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COMMENTS
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a(n) = number of independent vertex subsets (i.e. the Merrifield-Simmons index) of the normal alkyl radical of n carbons (i.e. CH_3(CH_2)_{n-1}).
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REFERENCES
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R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989. pp. 161-162.
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LINKS
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FORMULA
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a(n) = (8 - 5*sqrt(2))*(2 - 2*sqrt(2))^(n)/8 + (8 + 5*sqrt(2))*(2 + 2*sqrt(2))^(n)/8.
G.f.: x*(9+8*x)/(1-4*x-4*x^2).
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MAPLE
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a := proc (n) if n = 1 then 9 elif n = 2 then 44 else 4*a(n-1)+4*a(n-2) end if end proc: seq(a(n), n = 1 .. 25);
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MATHEMATICA
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LinearRecurrence[{4, 4}, {9, 44}, 30] (* Harvey P. Dale, Oct 30 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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