A083423 a(n) = (5*3^n + (-3)^n)/6.

1, 2, 9, 18, 81, 162, 729, 1458, 6561, 13122, 59049, 118098, 531441, 1062882, 4782969, 9565938, 43046721, 86093442, 387420489, 774840978, 3486784401, 6973568802, 31381059609, 62762119218, 282429536481, 564859072962, 2541865828329, 5083731656658, 22876792454961

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (0,9).

Formula

From Reinhard Zumkeller, Mar 04 2011: (Start)

G.f.: (1+2*x)/((1-3*x)*(1+3*x)).

E.g.f.: (5*exp(3*x) + exp(-3*x))/6.

a(n+3) = a(n+2)*a(n+1)/a(n). (End)

a(n) = 9*a(n-2). - Vincenzo Librandi, Mar 20 2011

From Amiram Eldar, Feb 17 2026: (Start)

Sum_{n>=0} 1/a(n) = 27/16.

Sum_{n>=0} (-1)^n/a(n) = 9/16. (End)

Mathematica

LinearRecurrence[{0, 9}, {1, 2}, 30] (* Harvey P. Dale, Dec 04 2019 *)

Crossrefs

Cf. A083424.

Sequence in context: A191520 A389060 A037421 * A068978 A006226 A109298

Adjacent sequences: A083420 A083421 A083422 * A083424 A083425 A083426

Keyword

easy,nonn

Author

Paul Barry, Apr 30 2003

Status

approved