A160869 a(n) = sigma(6^(n-1)).
1, 12, 91, 600, 3751, 22932, 138811, 836400, 5028751, 30203052, 181308931, 1088123400, 6529545751, 39179682372, 235085301451, 1410533397600, 8463265086751, 50779784492892, 304679288612371, 1828077476115000, 10968470088963751, 65810836228506612
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
- Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).
Programs
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Magma
[(2^n-1)*(3^n-1)/2: n in [1..50]]; // G. C. Greubel, Apr 30 2018
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Mathematica
Table[(2^n-1)*(3^n-1)/2,{n,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2010 *) LinearRecurrence[{12,-47,72,-36}, {1, 12, 91, 600}, 50] (* G. C. Greubel, Apr 30 2018 *) -
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
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PARI
for(n=1, 50, print1((2^n-1)*(3^n-1)/2, ", ")) \\ G. C. Greubel, Apr 30 2018
Formula
a(n) = A059387(n)/2. - Vladimir Joseph Stephan Orlovsky, Apr 28 2010
a(n) = 12*a(n-1)-47*a(n-2)+72*a(n-3)-36*a(n-4). - Colin Barker, Nov 24 2014
G.f.: -x*(6*x^2-1) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - Colin Barker, Nov 24 2014
Extensions
More terms from Vladimir Joseph Stephan Orlovsky, Apr 28 2010
More terms from Colin Barker, Nov 24 2014
Better definition from Altug Alkan, Oct 06 2015