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A109109
a(0)=1, a(1)=4, a(n) = 10a(n-1) + a(n-2).
1
1, 4, 41, 414, 4181, 42224, 426421, 4306434, 43490761, 439214044, 4435631201, 44795526054, 452390891741, 4568704443464, 46139435326381, 465963057707274, 4705770012399121, 47523663181698484, 479942401829383961, 4846947681475538094, 48949419216584764901
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. 284, K{Q_2(n)}).
FORMULA
a(n) = (1/2/sqrt(26))((sqrt(26)-1)(5+sqrt(26))^n+(sqrt(26)+1)(5-sqrt(26))^n).
G.f.: (1-6*x) / (1-10*x-x^2).
MAPLE
a:=n->(1/2/sqrt(26))*((sqrt(26)-1)*(5+sqrt(26))^n+(sqrt(26)+1)*(5-sqrt(26))^n): seq(expand(a(n)), n=0..20);
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==4, a[n]==10a[n-1]+a[n-2]}, a, {n, 20}] (* or *) LinearRecurrence[{10, 1}, {1, 4}, 50] (* Harvey P. Dale, Dec 03 2017 *)
PROG
(PARI) Vec((1-6*x)/(1-10*x-x^2) + O(x^100)) \\ Colin Barker, Oct 31 2014
CROSSREFS
Sequence in context: A121671 A089454 A193368 * A227996 A236528 A114467
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
EXTENSIONS
More terms from Colin Barker, Oct 31 2014
STATUS
approved