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A228597 The Wiener index of the graph obtained by applying Mycielski's construction to a benzenoid consisting of a linear chain of n hexagons.

%I A228597 #15 Sep 08 2022 08:46:05
%S A228597 141,445,941,1629,2509,3581,4845,6301,7949,9789,11821,14045,16461,
%T A228597 19069,21869,24861,28045,31421,34989,38749,42701,46845,51181,55709,
%U A228597 60429,65341,70445,75741,81229,86909,92781,98845,105101,111549,118189
%N A228597 The Wiener index of the graph obtained by applying Mycielski's construction to a benzenoid consisting of a linear chain of n hexagons.
%D A228597 D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
%H A228597 G. C. Greubel, <a href="/A228597/b228597.txt">Table of n, a(n) for n = 1..1000</a>
%H A228597 R. Balakrishnan, S. F. Raj, <a href="http://dx.doi.org/10.7151/dmgt.1509">The Wiener number of powers of the Mycielskian</a>, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).
%H A228597 B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://dx.doi.org/10.1002/(SICI)1097-461X(1996)60:5&lt;959::AID-QUA2&gt;3.0.CO;2-W">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.
%H A228597 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A228597 a(n) = 96*n^2 + 16*n + 29.
%F A228597 G.f.: x*(141+22*x+29*x^2)/(1-x)^3.
%F A228597 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _G. C. Greubel_, Dec 08 2016
%p A228597 a := proc (n) options operator, arrow: 96*n^2+16*n+29 end proc: seq(a(n), n = 1 .. 35);
%t A228597 LinearRecurrence[{3, -3, 1}, {141, 445, 941}, 100] (* or *) Table[96*n^2 + 16*n + 29 , {n,1,100}] (* _G. C. Greubel_, Dec 08 2016 *)
%o A228597 (PARI) Vec(x*(141+22*x+29*x^2)/(1-x)^3 + O(x^50)) \\ _G. C. Greubel_, Dec 08 2016
%o A228597 (Magma) [96*n^2+16*n+29: n in [1..40]]; // _Vincenzo Librandi_, Dec 09 2016
%Y A228597 Cf. A143937.
%K A228597 nonn,easy
%O A228597 1,1
%A A228597 _Emeric Deutsch_, Aug 27 2013