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%I A062396 #33 Sep 08 2022 08:45:03
%S A062396 2,10,82,730,6562,59050,531442,4782970,43046722,387420490,3486784402,
%T A062396 31381059610,282429536482,2541865828330,22876792454962,
%U A062396 205891132094650,1853020188851842,16677181699666570,150094635296999122
%N A062396 a(n) = 9^n + 1.
%H A062396 Vincenzo Librandi, <a href="/A062396/b062396.txt">Table of n, a(n) for n = 0..200</a>
%H A062396 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A062396 a(n) = 9*a(n-1) - 8 = A001019(n) + 1 = 10*a(n-1) - 9*a(n-2).
%F A062396 From _Mohammad K. Azarian_, Jan 02 2009: (Start)
%F A062396 G.f.: 1/(1-x) + 1/(1-9*x).
%F A062396 E.g.f.: e^x + e^(9*x). (End)
%t A062396 Table[9^n + 1, {n, 0, 20}]
%t A062396 LinearRecurrence[{10,-9},{2,10},20] (* _Harvey P. Dale_, May 30 2013 *)
%o A062396 (Magma) [9^n + 1: n in [0..35]]; // _Vincenzo Librandi_, Apr 30 2011
%o A062396 (PARI) a(n)=9^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A062396 Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062397, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081 for numbers one more than powers.
%K A062396 easy,nonn
%O A062396 0,1
%A A062396 _Henry Bottomley_, Jun 22 2001

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