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%I #16 Jun 23 2020 11:15:16
%S 74,86,110,158,254,446,830,1598,3134,6206,12350,24638,49214,98366,
%T 196670,393278,786494,1572926,3145790,6291518,12582974,25165886,
%U 50331710,100663358,201326654,402653246,805306430,1610612798,3221225534,6442451006,12884901950,25769803838,51539607614,103079215166,206158430270
%N a(n) = 12*2^n + 62.
%C a(n) (n>=1) is the number of vertices of the first type of dendrimer nanostar G[n], shown pictorially in the Iranmanesh et al. reference (Fig. 1).
%H Colin Barker, <a href="/A305265/b305265.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Iranmanesh, N. A. Gholami, <a href="https://hrcak.srce.hr/28365">Computing the Szeged index of two type dendrimer nanostars</a>, Croatica Chemica Acta, 81, No. 2, 2008, 299-303.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 30 2018: (Start)
%F G.f.: 2*(37 - 68*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F (End)
%p seq(12*2^n+62, n = 0..40);
%t Table[12*2^n+62,{n,0,50}] (* or *) LinearRecurrence[{3,-2},{74,86},50] (* _Harvey P. Dale_, Jun 23 2020 *)
%o (PARI) Vec(2*(37 - 68*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 30 2018
%Y Cf. A305266, A305267, A305268.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 29 2018
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