A109110 a(n) = 2a(n-1) + a(n-2) - a(n-3); a(0)=4, a(1)=9, a(2)=20.

4, 9, 20, 45, 101, 227, 510, 1146, 2575, 5786, 13001, 29213, 65641, 147494, 331416, 744685, 1673292, 3759853, 8448313, 18983187, 42654834, 95844542, 215360731, 483911170, 1087338529, 2443227497, 5489882353, 12335653674, 27717962204

Offset

0,1

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 (pp. 286, 288, K{S(n)})

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,1,-1)

Formula

G.f.: (4 + z - 2z^2)/(1 - 2z - z^2 + z^3).

a(n) = A052534(n+2). - R. J. Mathar, Feb 03 2014

Maple

a[0]:=4:a[1]:=9:a[2]:=20: for n from 3 to 32 do a[n]:=2*a[n-1]+a[n-2]-a[n-3] od: seq(a[n], n=0..32);

Mathematica

LinearRecurrence[{2, 1, -1}, {4, 9, 20}, 30] (* Harvey P. Dale, Apr 27 2025 *)

Crossrefs

Sequence in context: A019492 A020708 A345192 * A366726 A108870 A331942

Adjacent sequences: A109107 A109108 A109109 * A109111 A109112 A109113

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 19 2005

Status

approved