A304171 - OEIS

%I #20 May 11 2018 03:08:33

%S 49,136,310,658,1354,2746,5530,11098,22234,44506,89050,178138,356314,

%T 712666,1425370,2850778,5701594,11403226,22806490,45613018,91226074,

%U 182452186,364904410,729808858,1459617754,2919235546,5838471130,11676942298,23353884634,46707769306

%N a(n) = 87*2^n - 38 (n>=0).

%C a(n) is the number of vertices in the N-branched phenylacetylene NSB[n], shown pictorially in the Yarahmadi reference (for n=2).

%H Colin Barker, <a href="/A304171/b304171.txt">Table of n, a(n) for n = 0..1000</a>

%H Z. Yarahmadi and G. H. Fath-Tabar, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match65/n1/match65n1_201-208.pdf">The Wiener, Szeged, PI, Vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers</a>, MATCH: Commun. Math. Comput. Chem, 65 (2011) 201-208.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F From _Colin Barker_, May 10 2018: (Start)

%F G.f.: (49 - 11*x) / ((1 - x)*(1 - 2*x)).

%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

%F (End)

%p seq(87*2^n-38, n = 0 .. 35);

%o (PARI) Vec((49 - 11*x) / ((1 - x)*(1 - 2*x)) + O(x^30)) \\ _Colin Barker_, May 10 2018

%o (GAP) List([0..40],n->87*2^n-38); # _Muniru A Asiru_, May 10 2018

%Y Cf. A304172.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, May 10 2018