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%I #38 Feb 17 2024 10:28:53
%S 2,8,50,344,2402,16808,117650,823544,5764802,40353608,282475250,
%T 1977326744,13841287202,96889010408,678223072850,4747561509944,
%U 33232930569602,232630513987208,1628413597910450,11398895185373144
%N a(n) = 7^n + 1.
%H T. D. Noe, <a href="/A034491/b034491.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F a(n) = 7*a(n-1) - 6.
%F a(n) = 8*a(n-1) - 7*a(n-2).
%F From _Mohammad K. Azarian_, Jan 02 2009: (Start)
%F G.f.: 1/(1-x) + 1/(1-7*x).
%F E.g.f.: exp(x) + exp(7*x). (End)
%F a(n) = 2*A034494(n). - _G. C. Greubel_, Mar 11 2023
%t 7^Range[0,30] +1
%t LinearRecurrence[{8,-7},{2,8},20] (* _Harvey P. Dale_, Aug 18 2018 *)
%o (Sage) [sigma(7,n) for n in range(0,20)] # _Zerinvary Lajos_, Jun 04 2009
%o (PARI) a(n)=7^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Magma) [7^n +1: n in [0..30]]; // _G. C. Greubel_, Mar 11 2023
%Y Cf. A000051, A007689, A034472, A034474, A034494, A034524, A052539.
%Y Cf. A062394, A062395, A062396, A062397, A063376, A063481.
%Y Cf. A074600 - A074624, A178248, A228081.
%K easy,nonn
%O 0,1
%A _N. J. A. Sloane_
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