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A304167 a(n) = 3^n - 2^(n-1) + 2 (n>=1). 2

%I

%S 4,9,25,75,229,699,2125,6435,19429,58539,176125,529395,1590229,

%T 4774779,14332525,43013955,129074629,387289419,1161999325,3486260115,

%U 10459304629,31378962459,94138984525,282421147875,847271832229,2541832273899,7625530376125,22876658237235,68630108929429,205890595223739

%N a(n) = 3^n - 2^(n-1) + 2 (n>=1).

%C For n>=2, a(n) is the number of vertices of the Sierpinski Gasket Rhombus graph SR(n) (see Theorem 2.1 in the D. Antony Xavier et al. reference).

%H Colin Barker, <a href="/A304167/b304167.txt">Table of n, a(n) for n = 1..1000</a>

%H D. Antony Xavier, M. Rosary, and Andrew Arokiaraj, <a href="https://www.ijmsc.com/index.php/ijmsc/article/view/261">Topological properties of Sierpinski Gasket Rhombus graphs</a>, International J. of Mathematics and Soft Computing, 4, No. 2, 2014, 95-104.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

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

%F G.f.: x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>3.

%F (End)

%p seq(3^n-2^(n-1)+2, n = 1 .. 40);

%o (PARI) Vec(x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ _Colin Barker_, May 10 2018

%o (GAP) List([1..40],n->3^n-2^(n-1)+2); # _Muniru A Asiru_, May 10 2018

%Y Cf. A304168, A304169, A304170.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 10 2018

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Last modified April 24 12:21 EDT 2019. Contains 322429 sequences. (Running on oeis4.)