A165154 - OEIS

%I #33 Mar 08 2024 01:13:32

%S 0,1,91,9181,917371,91743661,9174307051,917431236541,91743118871131,

%T 9174311930159821,917431192628561611,91743119266342945501,

%U 9174311926602913490491,917431192660573778585581,91743119266054835992729771,9174311926605506476065432061

%N a(n) = 100*a(n-1) + (-9)^(n-1) for n>0, a(0)=0.

%H Vincenzo Librandi, <a href="/A165154/b165154.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (91,900).

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

%F a(n) = 91*a(n-1) + 900*a(n-2) for n>1, a(0)=0.

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

%F E.g.f.: (1/109)*(exp(100*x) - exp(-9*x)). - _G. C. Greubel_, Feb 09 2023

%t LinearRecurrence[{91,900}, {0,1}, 40] (* _G. C. Greubel_, Feb 09 2023 *)

%o (Magma) [(1/109)*(100^n-(-9)^n): n in [0..20]]; // _Vincenzo Librandi_, Jun 10 2011

%o (PARI) Vec(x/((1+9*x)*(1-100*x)) + O(x^20)) \\ _Colin Barker_, Oct 02 2015

%o (SageMath) [(100^n-(-9)^n)/109 for n in range(41)] # _G. C. Greubel_, Feb 09 2023

%Y Cf. A021113, A164913, A165155, A172162, A172163.

%K nonn,less,easy

%O 0,3

%A _Mark Dols_, Sep 05 2009

%E a(0) prepended by _Joerg Arndt_, Oct 02 2015