A221017 - OEIS

%I #23 Sep 08 2022 08:46:04

%S 47750,136534,559318,2753270,15400950,90898294,533474678,3033407350,

%T 16617791350,87925716854,451432421238,2259700922230,11073057240950,

%U 53297483364214,252669889754998,1182399069697910,5471583039141750,25074494578112374,113930964314371958

%N The hyper-Wiener index of the fullerenyl anion G[n]C[60], defined pictorially in the Arezoomand reference (see Fig. 5).

%C See Table on p. 722 of the Arezoomand reference.

%H G. C. Greubel, <a href="/A221017/b221017.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Arezoomand, <a href="http://www.chalcogen.ro/713_Dendrimer-Fullerene.pdf">On the distance-based topological indices of fullerene and fullerenyl anions having dendrimer units</a>, Digest J. of Nanomaterials and Biostructures, 4 (2009) 713-722.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (19,-150,636,-1560,2208,-1664,512).

%F a(n) = 14198+2^n*(-11544+6920*n+14000*n^2) +4^n*(6400*n^2-25600*n+45096).

%F G.f.: 2*(23875 -385358*x +2563836*x^2 -8881336*x^3 +17320448*x^4 -18447232*x^5 +7997440*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3). - _Bruno Berselli_, Dec 30 2012

%p a := proc (n) options operator, arrow: 14198+2^n*(-11544+6920*n+14000*n^2)+4^n*(6400*n^2-25600*n+45096) end proc: seq(a(n), n = 0 .. 18);

%t Table[14198 + 2^n (-11544 + 6920 n + 14000 n^2) + 4^n (6400 n^2 - 25600 n + 45096), {n, 0, 20}] (* _Vincenzo Librandi_, Nov 06 2018 *)

%o (PARI) a(n) = 14198+2^n*(-11544+6920*n+14000*n^2) + 4^n*(6400*n^2-25600*n+45096); \\ _Andrew Howroyd_, Nov 05 2018

%o (Magma) [14198 + 2^n*(-11544 + 6920*n + 14000*n^2) + 4^n*(6400*n^2 - 25600*n + 45096): n in [0..20]]; // _Vincenzo Librandi_, Nov 06 2018

%Y Cf. A221016.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Dec 30 2012