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A228603
a(1) = 9, a(2) = 44, a(n) = 4*(a(n-1) + a(n-2)) (n >=3).
0
9, 44, 212, 1024, 4944, 23872, 115264, 556544, 2687232, 12975104, 62649344, 302497792, 1460588544, 7052345344, 34051735552, 164416323584, 793872236544, 3833154240512, 18508105908224, 89365040594944, 431492586012672, 2083430506430464, 10059692369772544
OFFSET
1,1
COMMENTS
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}).
REFERENCES
R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989. pp. 161-162.
LINKS
H. Prodinger and R. F. Tichy, Fibonacci numbers of graphs, Fibonacci Quarterly, 20,1982, 16-21.
FORMULA
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).
a(n) = 9*A057087(n-1)+8*A057087(n-2). - R. J. Mathar, Nov 24 2013
MAPLE
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);
MATHEMATICA
LinearRecurrence[{4, 4}, {9, 44}, 30] (* Harvey P. Dale, Oct 30 2016 *)
CROSSREFS
Cf. A228602.
Sequence in context: A034558 A144109 A099867 * A297491 A104470 A282722
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 02 2013
STATUS
approved