|
|
A109114
|
|
a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6.
|
|
3
|
|
|
1, 6, 27, 117, 504, 2169, 9333, 40158, 172791, 743481, 3199032, 13764717, 59226489, 254838294, 1096512003, 4718045133, 20300689656, 87349312881, 375844495437, 1617174538542, 6958339206399, 29940172416369, 128825844462648
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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_{11}).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = ((sqrt(13) + 7)*((5 + sqrt(13))/2)^n + (sqrt(13) - 7)*((5 - sqrt(13))/2)^n)/(2*sqrt(13)).
G.f.: (1+z)/(1 - 5z + 3z^2).
|
|
MAPLE
|
a[0]:=1: a[1]:=6: for n from 2 to 26 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n], n=0..26);
|
|
MATHEMATICA
|
LinearRecurrence[{5, -3}, {1, 6}, 30] (* Harvey P. Dale, Dec 03 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|