A137195 Even-indexed coefficients related to Kirchhoff index of hexagonal (benzene) chains.

1, 6, 19, 64, 185, 542, 1511, 4144, 11329, 29894, 80731, 207696, 556217, 1405566, 3741263, 9328928, 24716353, 60998086, 161022115, 394136864, 1037382905, 2522256670, 6622609463, 16012527312, 41958312193, 100973218566

Offset: 0

Author

R. J. Mathar, Apr 04 2008

Keywords

• easy
• nonn

Comments

Essentially CONV transform of A079496.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Yujun Yang and Heping Zhang, Kirchhoff Index of linear hexagonal chains, Int. J. Quant. Chem. 108 (2008) 503-512.
• Index entries for linear recurrences with constant coefficients, signature (0,12,0,-38,0,12,0,-1).

Programs

Magma

I:=[1,6,19,64,185,542,1511,4144]; [n le 8 select I[n] else 12*Self(n-2)-38*Self(n-4)+12*Self(n-6)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2012

Mathematica

CoefficientList[Series[((1 + 3 x - x^2 - x^3)/(1 - 6 x^2 + x^4))^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)

Formula

O.g.f.: ((1+3*x-x^2-x^3)/(1-6*x^2+x^4))^2.

a(n) = 12*a(n-2)-38*a(n-4)+12*a(n-6)-a(n-8).