A103460 - OEIS

%I #21 Jun 29 2023 18:54:53

%S 1,10,82,730,6562,59050,531442,4782970,43046722,387420490,3486784402,

%T 31381059610,282429536482,2541865828330,22876792454962,

%U 205891132094650,1853020188851842,16677181699666570,150094635296999122

%N a(n) = 9^n + 1 - 0^n.

%C a(n)^3 is palindromic in base 9 (1_9, 1331_9, 1030301_9, 1003003001_9, ...).

%H G. C. Greubel, <a href="/A103460/b103460.txt">Table of n, a(n) for n = 0..1000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -9).

%F G.f.: (1-9*x^2)/((1-x)*(1-9*x)).

%F a(n) = Sum_{k=0..n} binomial(n, k)*0^(k*(n-k))*9^k.

%F a(n) = A062396(n), n > 0. - _R. J. Mathar_, Aug 28 2008

%F a(n) = 9*a(n-1) - 8, with a(1)=10. - _Vincenzo Librandi_, Dec 29 2010

%F E.g.f.: -1 + exp(x) + exp(9*x). - _G. C. Greubel_, Jun 26 2021

%t Table[9^n + 1 - Boole[n==0], {n,0,40}] (* _G. C. Greubel_, Jun 26 2021 *)

%o (Magma) [1] cat [9^n +1: n in [1..40]]; // _G. C. Greubel_, Jun 26 2021

%o (Sage) [1]+[9^n +1 for n in (1..40)] # _G. C. Greubel_, Jun 26 2021

%Y Cf. A046233, A062396.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 07 2005