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Even-indexed coefficients related to Kirchhoff index of hexagonal (benzene) chains.
1

%I #16 Apr 04 2024 09:49:52

%S 1,6,19,64,185,542,1511,4144,11329,29894,80731,207696,556217,1405566,

%T 3741263,9328928,24716353,60998086,161022115,394136864,1037382905,

%U 2522256670,6622609463,16012527312,41958312193,100973218566

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

%C Essentially CONV transform of A079496.

%H Vincenzo Librandi, <a href="/A137195/b137195.txt">Table of n, a(n) for n = 0..1000</a>

%H Yujun Yang and Heping Zhang, <a href="http://dx.doi.org/10.1002/qua.21537">Kirchhoff Index of linear hexagonal chains</a>, Int. J. Quant. Chem. 108 (2008) 503-512.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,12,0,-38,0,12,0,-1).

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

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

%t 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 *)

%o (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

%K easy,nonn

%O 0,2

%A _R. J. Mathar_, Apr 04 2008