A211866 (9^n - 5) / 4.

1, 19, 181, 1639, 14761, 132859, 1195741, 10761679, 96855121, 871696099, 7845264901, 70607384119, 635466457081, 5719198113739, 51472783023661, 463255047212959, 4169295424916641, 37523658824249779, 337712929418248021, 3039416364764232199, 27354747282878089801

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2013

Keywords

• nonn
• easy

Comments

(2*n, a(n)) are the solutions of Diophantine equation 3^x = 4*y + 5.

Second bisection of A080926. - Bruno Berselli, Feb 12 2013

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

Examples

			a(1) = 1;
a(2) = 9 + 1 + 9 = 19;
a(3) = 81 + 9 + 1 + 9 + 81 = 181;
a(4) = 729 + 81 + 9 + 1 + 9 + 81 + 729 = 1639; etc. - _Philippe Deléham_, Feb 24 2014
		

References

• Jiri Herman, Radan Kucera and Jaromir Simsa, Equations and Inequalities, Springer (2000), p. 225 (5.3).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A000792, A001019, A080926, A084222.

Programs

Haskell

a211866 = (flip div 4) . (subtract 5) . (9 ^)

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

Maple

A211866:=n->(9^n-5)/4; seq(A211866(n), n=1..50); # Wesley Ivan Hurt, Nov 13 2013

Mathematica

(9^Range[25] - 5)/4 (* Bruno Berselli, Feb 12 2013 *)
CoefficientList[Series[(1 + 9 x)/((1 - x) (1 - 9 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)

Maxima

makelist((9^n-5)/4,n,1,30); /* Martin Ettl, Feb 12 2013 */

PARI

a(n)=(9^n-5)/4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: x*(1+9*x)/((1-x)*(1-9*x)). - Bruno Berselli, Feb 12 2013

a(n)-a(n-1) = A000792(6n-4). - Bruno Berselli, Feb 12 2013

a(n) = 9*a(n-1) + 10, a(1) = 1. - Philippe Deléham, Feb 24 2014

a(n) = -A084222(2*n). - Philippe Deléham, Feb 24 2014