cp's OEIS Frontend

A193390 The hyper-Wiener index of a benzenoid consisting of a straight-line chain of n hexagons (s=2; see the Gutman et al. reference).

%I A193390 #27 Sep 08 2022 08:45:58
%S A193390 42,215,680,1661,3446,6387,10900,17465,26626,38991,55232,76085,102350,
%T A193390 134891,174636,222577,279770,347335,426456,518381,624422,745955,
%U A193390 884420,1041321,1218226,1416767,1638640,1885605,2159486,2462171,2795612,3161825,3562890,4000951,4478216
%N A193390 The hyper-Wiener index of a benzenoid consisting of a straight-line chain of n hexagons (s=2; see the Gutman et al. reference).
%H A193390 Vincenzo Librandi, <a href="/A193390/b193390.txt">Table of n, a(n) for n = 1..10000</a>
%H A193390 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 A193390 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 A193390 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A193390 a(n) = (8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3.
%F A193390 The Wiener-Hosoya polynomial is W(n,t) = (2*(t+1)*t^(2*n+2) - t^3 - 2*t^2 - 3*t + n*(t-1)*(t^2+1)*(t^2-t-4)+2)/(1-t)^2.
%F A193390 G.f.: x*(42 + 5*x + 25*x^2 - 9*x^3 + x^4)/(1-x)^5. - _Bruno Berselli_, Jul 27 2011
%p A193390 a := proc (n) options operator, arrow: (8/3)*n^4+(32/3)*n^3+(46/3)*n^2+(37/3)*n+1 end proc; seq(a(n), n = 1 .. 35);
%o A193390 (Magma) [(8*n^4 + 32*n^3 + 46*n^2 + 37*n + 3)/3: n in [1..30]]; // _Vincenzo Librandi_, Jul 26 2011
%o A193390 (PARI) a(n)=(8*n^4+32*n^3+46*n^2+37*n)/3+1 \\ _Charles R Greathouse IV_, Jul 26 2011
%Y A193390 Cf. A143937, A143938.
%K A193390 nonn,easy
%O A193390 1,1
%A A193390 _Emeric Deutsch_, Jul 25 2011