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

Author

Emeric Deutsch, Jun 19 2005

Keywords

• nonn
• easy

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

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

Programs

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 *)

Formula

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

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