A102345 a(n) = 3^n + (-1)^n.

2, 2, 10, 26, 82, 242, 730, 2186, 6562, 19682, 59050, 177146, 531442, 1594322, 4782970, 14348906, 43046722, 129140162, 387420490, 1162261466, 3486784402, 10460353202, 31381059610, 94143178826, 282429536482, 847288609442

Offset: 0

Author

Graeme McRae, Feb 16 2005

Keywords

• easy
• nonn

Comments

a(n) = A105723(n) + 2*(-1)^n; (a(n) + A105723(n))/2 = A000244(n). - Reinhard Zumkeller, Apr 18 2005

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..2095
• Weerayuth Nilsrakoo and Achariya Nilsrakoo, On One-Parameter Generalization of Jacobsthal Numbers, WSEAS Trans. Math. (2025) Vol. 24, 51-61. See p. 3.
• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Apart from leading term, same as A084182.

Cf. A000244, A046717, A105723.

Programs

Mathematica

Table[3^n+(-1)^n,{n,0,30}] (* or *) LinearRecurrence[{2,3},{2,2},30] (* Harvey P. Dale, Jun 19 2016 *)

Sage

[lucas_number2(n,2,-3) for n in range(0, 26)] # Zerinvary Lajos, Apr 30 2009

Formula

a(n) = 2*a(n-1) + 3*a(n-2).

From Elmo R. Oliveira, Dec 18 2023: (Start)

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

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

a(n) = 2*A046717(n). (End)