A109109 a(0)=1, a(1)=4, a(n) = 10a(n-1) + a(n-2).

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)}).

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