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%I #25 Sep 08 2022 08:45:45
%S 1,12,91,600,3751,22932,138811,836400,5028751,30203052,181308931,
%T 1088123400,6529545751,39179682372,235085301451,1410533397600,
%U 8463265086751,50779784492892,304679288612371,1828077476115000,10968470088963751,65810836228506612
%N a(n) = sigma(6^(n-1)).
%H Colin Barker, <a href="/A160869/b160869.txt">Table of n, a(n) for n = 1..1000</a>
%H J. H. Kwak and J. Lee, <a href="https://doi.org/10.1142/9789812799890_0005">Enumeration of graph coverings, surface branched coverings and related group theory</a>, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F a(n) = A059387(n)/2. - _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010
%F a(n) = 12*a(n-1)-47*a(n-2)+72*a(n-3)-36*a(n-4). - _Colin Barker_, Nov 24 2014
%F G.f.: -x*(6*x^2-1) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Nov 24 2014
%F a(n) = A000203(A000400(n-1)). - _Michel Marcus_, Sep 18 2018
%t Table[(2^n-1)*(3^n-1)/2,{n,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%t LinearRecurrence[{12,-47,72,-36}, {1, 12, 91, 600}, 50] (* _G. C. Greubel_, Apr 30 2018 *)
%o (PARI) Vec(-x*(6*x^2-1)/((x-1)*(2*x-1)*(3*x-1)*(6*x-1)) + O(x^100)) \\ _Colin Barker_, Nov 24 2014
%o (PARI) for(n=1, 50, print1((2^n-1)*(3^n-1)/2, ", ")) \\ _G. C. Greubel_, Apr 30 2018
%o (Magma) [(2^n-1)*(3^n-1)/2: n in [1..50]]; // _G. C. Greubel_, Apr 30 2018
%Y Row 6 of array in A160870.
%Y Cf. A000203, A000400, A059387.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Nov 15 2009
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010
%E More terms from _Colin Barker_, Nov 24 2014
%E Better definition from _Altug Alkan_, Oct 06 2015
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