A172174 - OEIS

%I #21 Mar 04 2024 01:13:26

%S 1,91,8191,737191,66347191,5971247191,537412247191,48367102247191,

%T 4353039202247191,391773528202247191,35259617538202247191,

%U 3173365578438202247191,285602902059438202247191,25704261185349438202247191,2313383506681449438202247191

%N a(n) = 90*a(n-1) + 1.

%C Difference of pairs of integers given in A162849.

%C Sum of digits give A017173.

%H Colin Barker, <a href="/A172174/b172174.txt">Table of n, a(n) for n = 1..512</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (91,-90).

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

%F a(n) = 91*a(n-1) - 90*a(n-2) for n>2.

%F G.f.: 1 / ((1-x)*(1-90*x)). (End)

%t NestList[90#+1&,1,20] (* _Harvey P. Dale_, Aug 29 2014 *)

%o (PARI) Vec(1/((x-1)*(90*x-1)) + O(x^30)) \\ _Colin Barker_, Oct 02 2015

%o (SageMath) [(90^n -1)/89 for n in (1..50)] # _G. C. Greubel_, Apr 26 2022

%Y Cf. A017173, A162849, A165154.

%K nonn,easy

%O 1,2

%A _Mark Dols_, Jan 28 2010