A172163 - OEIS

%I #18 Apr 25 2022 08:02:29

%S 0,0,10,1020,103030,10307040,1030814050,103082025060,10308214641070,

%T 1030821549763080,103082156348992090,10308215646124529100,

%U 1030821564770799275110,103082156478507926931120,10308215647869324982098130,1030821564787110934730377140

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

%H Colin Barker, <a href="/A172163/b172163.txt">Table of n, a(n) for n = 0..501</a>

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

%F a(n) = 10^(2*n+1)/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>2.

%F G.f.: 10*x^2 / ((1+9*x)*(1-11*x)*(1-100*x)).

%F (End)

%t Table[10^(2 n + 1)/9701 - 11^n/178 + (-9)^n/218, {n, 0, 20}] (* _Bruno Berselli_, Oct 02 2015 *)

%t LinearRecurrence[{102,-101,-9900},{0,0,10},20] (* _Harvey P. Dale_, Aug 17 2021 *)

%o (PARI) concat([0,0], Vec(10*x^2/((9*x+1)*(11*x-1)*(100*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 02 2015

%o (SageMath) [(89*(-9)^n + 2*10^(2*n+1) - 109*11^n)/19402 for n in (0..50)] # _G. C. Greubel_, Apr 24 2022

%Y Cf. A162741, A162849, A165154, A165155, A172162.

%K nonn,easy

%O 0,3

%A _Mark Dols_, Jan 27 2010

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