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The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Ashrafi et al. reference.
1

%I #18 Nov 15 2016 03:02:16

%S 657339,15126495,170253735,1399219767,9656453079,59728974615,

%T 342996234135,1867389894807,9768453728919,49540857757335,

%U 245123724445335,1188721211741847,5669374461982359,26661906782549655,123891350653597335,569765357115700887,2596763217388533399

%N The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Ashrafi et al. reference.

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

%H A. R. Ashrafi and M. Mirzagar, <a href="http://nopr.niscair.res.in/handle/123456789/2084">PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers</a>, Indian J. of Chemistry, 47A, 2008, 538-541.

%H M. Rostami, M. Shabanian, and H. Moghanian, <a href="http://www.chalcogen.ro/247_Rostami.pdf">Some topological indices for theoretical study of two types of nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.

%H J. Yang, F. Xia, and S. Chen, <a href="http://www.m-hikari.com/ijcms-2011/5-8-2011/yangjgIJCMS5-8-2011-2.pdf">Second-order and third-order connectivity indices of an infinite family of dendrimer nanostars</a>, Int. J. Contemp. Math. Sciences, 6, 2011, No. 5, 215-220.

%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) = -685719 - 2949654*2^n + 2264412*4^n + 495780*n*2^n - 1584720*n*4^n - 136500*n^2*2^n + 608400*n^2*4^n.

%F G.f.: -3*x*(81408*x^6 +1294464*x^5 +4778592*x^4 +5101816*x^3 -6182940*x^2 +879018*x +219113) / ((x -1)*(2*x -1)^3*(4*x -1)^3). - _Colin Barker_, Apr 01 2013

%p a := proc (n) options operator, arrow: 685719-2949654*2^n+2264412*4^n-1584720*4^n*n+495780*2^n*n-136500*2^n*n^2+608400*4^n*n^2 end proc: seq(a(n), n = 1 .. 17);

%Y Cf. A216122.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Mar 25 2013