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%I #20 Sep 12 2024 19:10:19
%S 2,21,221,2331,24641,261051,2771561,29487171,314358881,3357947691,
%T 35937424601,385311670611,4138428376721,44522712143931,
%U 479749833583241,5177248169415651,55949729863572161,605447028499293771,6559917313492231481,71159090448414546291,772749994932560009201
%N a(n) = 10^n + 11^n.
%C a(n) gives the combined total number of n digit numbers [preceding zeros allowed] in base 10 and 11.
%H Vincenzo Librandi, <a href="/A155872/b155872.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (21,-110).
%F G.f.: 1/(1-10*x) + 1/(1-11*x). - _Vincenzo Librandi_, Feb 06 2013
%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)
%F E.g.f.: exp(10*x)*(exp(x) + 1).
%F a(n) = 21*a(n-1) - 110*a(n-2) for n > 1. (End)
%t CoefficientList[Series[1/(1 - 10 x) + 1/(1 - 11 x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 06 2013 *)
%t LinearRecurrence[{21,-110},{2,21},20] (* _Harvey P. Dale_, Aug 27 2020 *)
%o (Magma) [10^n+11^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 06 2013
%K nonn,easy
%O 0,1
%A Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 29 2009