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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS KekulĂ© numbers for certain benzenoids. REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 284, K{Q_2(n)}). LINKS Colin Barker, Table of n, a(n) for n = 0..900 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (10,1). 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 Adjacent sequences:  A109106 A109107 A109108 * A109110 A109111 A109112 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 19 2005 EXTENSIONS More terms from Colin Barker, Oct 31 2014 STATUS approved

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Last modified July 20 04:21 EDT 2018. Contains 312799 sequences. (Running on oeis4.)