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.
Index entries for linear recurrences with constant coefficients, signature (4,4).
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).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 02 2013
STATUS
approved