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A114481 Kekulé numbers for certain benzenoids. 0
5, 105, 2331, 52137, 1167291, 26137809, 585284211, 13105857753, 293470347915, 6571477451169, 147150526244067, 3295039441438377, 73783527649203195, 1652183243687500785, 36996190853123920851, 828429983702209723257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).

LINKS

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (27,-108,108).

FORMULA

a(n) = (3^(n+1) + (12 + 6*sqrt(3))^(n+1)/4 + (12 - 6*sqrt(3))^(n+1)/4)/27.

From Colin Barker, Aug 30 2013: (Start)

a(n) = 27*a(n-1) - 108*a(n-2) + 108*a(n-3).

G.f.: -x*(36*x^2 - 30*x + 5) / ((3*x-1)*(36*x^2 - 24*x + 1)). (End)

MAPLE

a:=n->(3^(n+1)+(12+6*sqrt(3))^(n+1)/4+(12-6*sqrt(3))^(n+1)/4)/27: seq(expand(a(n)), n=1..18);

CROSSREFS

Sequence in context: A327273 A034225 A273966 * A273962 A223043 A200851

Adjacent sequences:  A114478 A114479 A114480 * A114482 A114483 A114484

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 30 2005

STATUS

approved

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)