Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 Feb 13 2024 03:36:08
%S 2,19,181,1729,16561,159049,1531441,14782969,143046721,1387420489,
%T 13486784401,131381059609,1282429536481,12541865828329,
%U 122876792454961,1205891132094649,11853020188851841
%N a(n) = 9^n + 10^n.
%H Vincenzo Librandi, <a href="/A221904/b221904.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19,-90).
%F G.f.: 1/(1 - 9*x) + 1/(1 - 10*x).
%F E.g.f.: exp(9*x) + exp(10*x).
%F a(n) = 19*a(n-1) - 90*a(n-2), a(1)=2, a(2)=19.
%t CoefficientList[Series[1/(1-9*x) + 1/(1-10*x), {x, 0, 30}], x]
%t LinearRecurrence[{19,-90},{2,19},30] (* _Harvey P. Dale_, Nov 10 2017 *)
%o (Magma) [9^n + 10^n: n in [0..30]];
%Y Cf. A007689, A074611, A074615, A074619, A074622, A074624, A155872.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Feb 06 2013