A227496 - OEIS

%I #34 Oct 21 2024 12:00:31

%S 58278,386154,2197138,11480034,56846210,271400130,1262261058,

%T 5756835906,25860706882,114780464706,504480353858,2199370440258,

%U 9523306249794,40996576329282,175599810575938,748853449588290,3181230972730946,13468193224392258

%N The Wiener index of the nanostar dendrimer defined pictorially as NS_3 in the Ashrafi et al. references.

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

%H Vincenzo Librandi, <a href="/A227496/b227496.txt">Table of n, a(n) for n = 1..1001</a> [Offset shifted to 1 by _Georg Fischer_, Aug 19 2021]

%H A. R. Ashrafi and P. Nikzad, <a href="https://chalcogen.ro/269_AshrafiNikzad.pdf">Connectivity index of the family of dendrimer nanostars</a>, Digest J. Nanomaterials and Biostructures, 4, 2009, 269-273.

%H A. R. Ashrafi and P. Nikzad, <a href="https://chalcogen.ro/383_Ashrafi.pdf">Kekulé index and bounds of energy for nanostar dendrimers</a>, Digest J. Nanomaterials and Biostructures, 4, 2009, 383-388.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,-64,148,-160,64).

%F a(n) = -446 + 2^n*(5338 - 208*n) + 4^n*(1300 + 10816*n).

%F G.f.: 2*x*(29139 - 185730*x + 453464*x^2 - 497024*x^3 + 198144*x^4) / ((1-x)*(1-2*x)^2*(1-4*x)^2).

%p a := n -> -446+2^n*(5338-208*n)+4^n*(1300+10816*n): seq(a(n), n = 1..18);

%t gf := -(58278 x + 4 x^2 (-92865 + 4 x (56683 + 16 x (-3883 + 1548 x)))) / ((-1 + x) (1 - 6 x + 8 x^2)^2); ser := Series[gf, {x, 0, 18}];

%t Table[Coefficient[ser, x, n], {n, 1, 18}] (* Vincenzo Librandi, Jul 20 2013 *)

%t LinearRecurrence[{13,-64,148,-160,64},{58278,386154,2197138,11480034,56846210},20] (* _Harvey P. Dale_, Oct 21 2024 *)

%o (Magma) [-446 + 2^n*(5338 - 208*n) + 4^n*(1300 + 10816*n): n in [1..20]]; // _Vincenzo Librandi_, Jul 20 2013

%Y Cf. A227497.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Jul 19 2013