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a(n) = ( A165154(n) + A165155(n) )/2.
3

%I #18 Apr 25 2022 08:01:50

%S 0,1,101,10201,1020401,102050701,10205121101,1020513261601,

%T 102051333512201,10205133479922901,1020513348977553701,

%U 102051334912467474601,10205133491373712765601,1020513349139081705516701,102051334913924160974827901,10205133491392617410795809201

%N a(n) = ( A165154(n) + A165155(n) )/2.

%H Colin Barker, <a href="/A172162/b172162.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (102,-101,-9900).

%F a(n) = 99*100^n/9701 - 11^n/178 - (-9)^n/218. [_Bruno Berselli_, Oct 02 2015]

%F From _Colin Barker_, Oct 02 2015: (Start)

%F a(n) = 102*a(n-1) - 101*a(n-2) - 9900*a(n-3) for n>3.

%F G.f.: x*(1-x) / ((1+9*x)*(1-11*x)*(1-100*x)).

%F (End)

%t Table[99 100^n/9701 - 11^n/178 - (-9)^n/218, {n, 0, 20}] (* _Bruno Berselli_, Oct 02 2015 *)

%o (PARI) concat(0, Vec(-x*(x-1)/((9*x+1)*(11*x-1)*(100*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 02 2015

%o (SageMath) [(-89*(-9)^n - 109*11^n + 198*10^(2*n))/19402 for n in (0..50)] # _G. C. Greubel_, Apr 24 2022

%Y Cf. A162741, A162849, A165154, A165155, A172163.

%K nonn,easy

%O 0,3

%A _Mark Dols_, Jan 27 2010

%E a(0) and more terms added by _Bruno Berselli_, Oct 02 2015