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A109115
a(n) = 4*a(n-1) + 3*a(n-2), a(0)=1, a(1)=6.
3
1, 6, 27, 126, 585, 2718, 12627, 58662, 272529, 1266102, 5881995, 27326286, 126951129, 589783374, 2739986883, 12729297654, 59137151265, 274736498022, 1276357445883, 5929639277598, 27547629448041, 127979435624958
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 302, P_{12}).
FORMULA
a(n) = ((sqrt(7) + 4)*(2 + sqrt(7))^n + (sqrt(7) - 4)*(2 - sqrt(7))^n)/(2*sqrt(7)).
G.f.: (1+2z)/(1 - 4z - 3z^2).
a(n) = A015530(n+1)+2*A015530(n). - R. J. Mathar, Jul 26 2022
MAPLE
a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=4*a[n-1]+3*a[n-2] od: seq(a[n], n=0..26);
MATHEMATICA
LinearRecurrence[{4, 3}, {1, 6}, 40] (* Harvey P. Dale, Aug 20 2020 *)
CROSSREFS
Sequence in context: A045500 A360057 A377263 * A038176 A104745 A184279
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved