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%I #61 Feb 08 2024 01:36:52
%S 2,6,26,126,626,3126,15626,78126,390626,1953126,9765626,48828126,
%T 244140626,1220703126,6103515626,30517578126,152587890626,
%U 762939453126,3814697265626,19073486328126,95367431640626,476837158203126
%N a(n) = 5^n + 1.
%C a(n) is the deficiency of 3*5^n (see A033879). - _Patrick J. McNab_, May 28 2017
%H T. D. Noe, <a href="/A034474/b034474.txt">Table of n, a(n) for n = 0..200</a>
%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].
%H Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).
%F a(n) = 5*a(n-1) - 4 with a(0) = 2.
%F a(n) = 6*a(n-1) - 5*a(n-2) for n > 1.
%F From _Mohammad K. Azarian_, Jan 02 2009: (Start)
%F G.f.: 1/(1-x) + 1/(1-5*x) = (2-6*x)/((1-x)*(1-5*x)).
%F E.g.f.: exp(x) + exp(5*x). (End)
%F a(n) = A279396(n+5,5). - _Wolfdieter Lang_, Jan 10 2017
%F From _Elmo R. Oliveira_, Dec 06 2023: (Start)
%F a(n) = A000351(n) + 1.
%F a(n) = 2*A034478(n). (End)
%e G.f. = 2 + 6*x + 26*x^2 + 126*x^3 + 626*x^4 + 3126*x^5 + 15626*x^6 + ...
%t Table[5^n + 1, {n, 0, 25}]
%t LinearRecurrence[{6,-5},{2,6},30] (* _Harvey P. Dale_, Jul 29 2015 *)
%o (Sage) [lucas_number2(n,6,5) for n in range(25)] # _Zerinvary Lajos_, Jul 08 2008
%o (Sage) [sigma(5,n) for n in range(25)] # _Zerinvary Lajos_, Jun 04 2009
%o (Sage) [5^n+1 for n in range(30)] # _Bruno Berselli_, Jan 11 2017
%o (PARI) a(n)=5^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Magma) [5^n+1: n in [0..30]]; // _Vincenzo Librandi_, Jan 11 2017
%Y Cf. A000051, A000351, A007689, A024049, A033879, A034472, A034478, A034491, A034524, A052539, A062394, A062395, A062396, A062397, A063376, A063481, A074600-A074624, A178248, A228081, A279396.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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