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A211866 (9^n - 5) / 4.

%I A211866 #31 Sep 08 2022 08:46:02
%S A211866 1,19,181,1639,14761,132859,1195741,10761679,96855121,871696099,
%T A211866 7845264901,70607384119,635466457081,5719198113739,51472783023661,
%U A211866 463255047212959,4169295424916641,37523658824249779,337712929418248021,3039416364764232199,27354747282878089801
%N A211866 (9^n - 5) / 4.
%C A211866 (2*n, a(n)) are the solutions of Diophantine equation 3^x = 4*y + 5.
%C A211866 Second bisection of A080926. - _Bruno Berselli_, Feb 12 2013
%C A211866 Sum of n-th row of triangle of powers of 9: 1; 9 1 9; 81 9 1 9 81; 729 81 9 1 9 81 729; ... - _Philippe Deléham_, Feb 24 2014
%D A211866 Jiri Herman, Radan Kucera and Jaromir Simsa, Equations and Inequalities, Springer (2000), p. 225 (5.3).
%H A211866 Vincenzo Librandi, <a href="/A211866/b211866.txt">Table of n, a(n) for n = 1..200</a>
%H A211866 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A211866 G.f.:  x*(1+9*x)/((1-x)*(1-9*x)). - _Bruno Berselli_, Feb 12 2013
%F A211866 a(n)-a(n-1) = A000792(6n-4). - _Bruno Berselli_, Feb 12 2013
%F A211866 a(n) = 9*a(n-1) + 10, a(1) = 1. - _Philippe Deléham_, Feb 24 2014
%F A211866 a(n) = -A084222(2*n). - _Philippe Deléham_, Feb 24 2014
%e A211866 a(1) = 1;
%e A211866 a(2) = 9 + 1 + 9 = 19;
%e A211866 a(3) = 81 + 9 + 1 + 9 + 81 = 181;
%e A211866 a(4) = 729 + 81 + 9 + 1 + 9 + 81 + 729 = 1639; etc. - _Philippe Deléham_, Feb 24 2014
%p A211866 A211866:=n->(9^n-5)/4; seq(A211866(n), n=1..50); # _Wesley Ivan Hurt_, Nov 13 2013
%t A211866 (9^Range[25] - 5)/4 (* _Bruno Berselli_, Feb 12 2013 *)
%t A211866 CoefficientList[Series[(1 + 9 x)/((1 - x) (1 - 9 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 26 2014 *)
%o A211866 (Haskell)
%o A211866 a211866 = (flip div 4) . (subtract 5) . (9 ^)
%o A211866 (Maxima) makelist((9^n-5)/4,n,1,30); /* _Martin Ettl_, Feb 12 2013 */
%o A211866 (Magma) I:=[1,19]; [n le 2 select I[n] else 10*Self(n-1)-9*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Feb 26 2014
%o A211866 (PARI) a(n)=(9^n-5)/4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A211866 Cf. A000792, A001019, A080926, A084222.
%K A211866 nonn,easy
%O A211866 1,2
%A A211866 _Reinhard Zumkeller_, Feb 12 2013