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A193400 Hyper-Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

%I A193400 #29 Sep 08 2022 08:45:58
%S A193400 42,215,636,1513,2862,5211,8352,13229,19314,28063,38532,52785,69366,
%T A193400 91043,115752,147061,182202,225639,273804,332153,396222,472555,555696,
%U A193400 653373,759042,881711,1013652,1165249,1327494,1512243,1709112,1931525,2167626,2432503,2712732
%N A193400 Hyper-Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).
%H A193400 Vincenzo Librandi, <a href="/A193400/b193400.txt">Table of n, a(n) for n = 1..10000</a>
%H A193400 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 A193400 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 A193400 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A193400 a(n) = ( 6*n^4 +40*n^3 +114*n^2 +16*n -45 +(-1)^n*(6*n^2 +20*n -63) )/4.
%F A193400 G.f.: x*(42+131*x+122*x^2+63*x^3-146*x^4+25*x^5+78*x^6-27*x^7)/((1+x)^3*(1-x)^5). - _Bruno Berselli_, Jul 27 2011
%p A193400 a := proc (n) options operator, arrow: (3/2)*n^4+10*n^3+(57/2)*n^2+4*n-45/4+(1/4)*(-1)^n*(6*n^2+20*n-63) end proc: seq(a(n), n = 1 .. 35);
%o A193400 (Magma) [(6*n^4 + 40*n^3 + 114*n^2 + 16*n - 45 + (-1)^n*(6*n^2 +20*n -63))/4: n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193400 (PARI) a(n)=(6*n^4+40*n^3+114*n^2+16*n-45+(-1)^n*(6*n^2+20*n-63))/4 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A193400 Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397, A193398, A193399.
%K A193400 nonn,easy
%O A193400 1,1
%A A193400 _Emeric Deutsch_, Jul 25 2011