A227710 - OEIS

%I #11 Sep 08 2022 08:46:05

%S 47160,501516,3609684,21645828,117137700,594466020,2889375588,

%T 13620124260,62765849700,284277930084,1270122831972,5612855201892,

%U 24581542031460,106848038187108,461482510708836,1982297444839524

%N The Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference.

%C a(1) has been checked by the direct computation of the Wiener index (using Maple).

%D A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, 2011, 1075-1080.

%H Vincenzo Librandi, <a href="/A227710/b227710.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 4^n*(31752*n-46494)+2^n*(3276*n+51786)-3996.

%F G.f.: 36*x*(1310-3099*x+3006*x^2-4520*x^3+2304*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

%p a := proc (n) options operator, arrow: 4^n*(31752*n-46494)+2^n*(3276*n+51786)-3996 end proc: seq(a(n), n = 1 .. 20);

%t CoefficientList[Series[36 (1310 - 3099 x + 3006 x^2 - 4520 x^3 + 2304 x^4) / ((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 04 2013 *)

%o (Magma) [(4^n*(31752*n-46494)+2^n*(3276*n+51786))-3996: n in [1..20]]; // _Vincenzo Librandi_, Aug 04 2013

%Y Cf. A227711.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Aug 03 2013