%I #29 Sep 09 2024 21:05:51
%S 1,18,99,756,6597,59094,531495,4783032,43046793,387420570,3486784491,
%T 31381059708,282429536589,2541865828446,22876792455087,
%U 205891132094784,1853020188851985,16677181699666722,150094635296999283,1350851717672992260,12157665459056928981
%N a(n) = 9^n + 9*n.
%H Vincenzo Librandi, <a href="/A221911/b221911.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-19,9).
%F G.f.: (1+7*x-80*x^2)/((1-x)^2*(1-9*x)).
%F a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
%F E.g.f.: exp(x)*(exp(8*x) + 9*x). - _Elmo R. Oliveira_, Sep 09 2024
%t Table[(9^n + 9 n), {n, 0, 25}] (* or *) CoefficientList[Series[(1 + 7 x - 80 x^2)/((1 - x)^2 (1 - 9 x)), {x, 0, 30}], x]
%t LinearRecurrence[{11,-19,9},{1,18,99},20] (* _Harvey P. Dale_, Aug 18 2014 *)
%o (Magma) [9^n + 9*n: n in [0..25]]; /* or */ I:=[1, 18, 99]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]];
%o (PARI) a(n)=9^n+9*n \\ _Charles R Greathouse IV_, Apr 18 2013
%Y Cf. A198399, A226202, A370663.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Mar 03 2013