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
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
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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
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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).
Comments