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A137195 Even-indexed coefficients related to Kirchhoff index of hexagonal (benzene) chains. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Essentially CONV transform of A079496.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Yujun Yang, 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).

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).

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 *)

PROG

(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

CROSSREFS

Sequence in context: A184189 A152098 A041673 * A055916 A266472 A259804

Adjacent sequences:  A137192 A137193 A137194 * A137196 A137197 A137198

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Apr 04 2008

STATUS

approved

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Last modified September 29 16:23 EDT 2022. Contains 357090 sequences. (Running on oeis4.)