cp's OEIS Frontend

A226202 a(n) = 9^n + n.

%I A226202 #30 Feb 03 2025 18:59:15
%S A226202 1,10,83,732,6565,59054,531447,4782976,43046729,387420498,3486784411,
%T A226202 31381059620,282429536493,2541865828342,22876792454975,
%U A226202 205891132094664,1853020188851857,16677181699666586,150094635296999139,1350851717672992108,12157665459056928821,109418989131512359230
%N A226202 a(n) = 9^n + n.
%C A226202 After 83, the next prime of this form is a(76). - _Bruno Berselli_, Jun 18 2013
%H A226202 Vincenzo Librandi, <a href="/A226202/b226202.txt">Table of n, a(n) for n = 0..300</a>
%H A226202 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-19,9).
%F A226202 G.f.: (-1+x+8*x^2)/((9*x-1)*(x-1)^2).
%F A226202 a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
%F A226202 E.g.f.: exp(x)*(exp(8*x) + x). - _Elmo R. Oliveira_, Sep 09 2024
%t A226202 Table[9^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(- 1 + x + 8 x^2) / ((9 x - 1) (x - 1)^2), {x, 0, 30}], x]
%t A226202 LinearRecurrence[{11,-19,9},{1,10,83},20] (* _Harvey P. Dale_, Feb 03 2016 *)
%o A226202 (Magma) [9^n+n: n in [0..30]];
%o A226202 (Magma) I:=[1, 10, 83]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]];
%o A226202 (PARI) a(n)=9^n+n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A226202 Cf. numbers of the form k^n + n: A006127 (k=2), A104743 (k=3), A158879 (k=4), A104745 (k=5), A226200 (k=6), A226199 (k=7), A226201 (k=8), this sequence (k=9), A081552 (k=10), A226737 (k=11).
%Y A226202 Cf. A199677 (first differences).
%K A226202 nonn,easy
%O A226202 0,2
%A A226202 _Vincenzo Librandi_, Jun 16 2013