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A193396 Hyper-Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).

%I A193396 #28 Sep 08 2022 08:45:58
%S A193396 215,636,1557,3162,5875,10008,16113,24630,36239,51508,71245,96146,
%T A193396 127147,165072,210985,265838,330823,407020,495749,598218,715875,
%U A193396 850056,1002337,1174182,1367295,1583268,1823933,2091010,2386459,2712128,3070105,3462366,3891127,4358492
%N A193396 Hyper-Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).
%H A193396 Vincenzo Librandi, <a href="/A193396/b193396.txt">Table of n, a(n) for n = 2..10000</a>
%H A193396 A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, <a href="http://www.fmf.uni-lj.si/~klavzar/preprints/Wiener-survey.pdf">Wiener Index of Hexagonal Systems</a>, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
%H A193396 I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match43/match43_49-66.pdf">On Hosoya polynomials of benzenoid graphs</a>, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
%H A193396 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F A193396 a(n) = (8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3.
%F A193396 G.f.: x^2*(215 - 224*x + 88*x^2 + 114*x^3 - 63*x^4 - 2*x^5)/((1+x)*(1-x)^5). - _Bruno Berselli_, Jul 27 2011
%p A193396 a := proc (n) options operator, arrow: (8/3)*n^4+8*n^3+(28/3)*n^2+71*n+11*(-1)^n-82 end proc: seq(a(n), n = 2 .. 35);
%o A193396 (Magma) [(8*n^4 + 24*n^3 + 28*n^2 + 213*n + 33*(-1)^n - 246)/3: n in [2..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193396 (PARI) a(n)=(8*n^4+24*n^3+28*n^2+213*n+33*(-1)^n-246)/3 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A193396 Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395.
%K A193396 nonn,easy
%O A193396 2,1
%A A193396 _Emeric Deutsch_, Jul 25 2011