A084182 a(n) = 3^n + (-1)^n - [1/(n+1)], where [] represents the floor function.

1, 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, 2541865828330, 7625597484986

Offset: 0

Author

Paul Barry, May 19 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A084181.

From Peter Bala, Dec 26 2012: (Start)

Let F(x) = product {n >= 0} (1 - x^(3*n+1))/(1 - x^(3*n+2)). This sequence is the simple continued fraction expansion of the real number F(-1/3) = 1.47627 73316 74531 44215 ... = 1 + 1/(2 + 1/(10 + 1/(26 + 1/(82 + ...)))). See A111317.

(End)

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Except for leading term, same as A102345.

Cf. A046717, A111317.

Programs

Mathematica

LinearRecurrence[{2,3},{1,2,10},30] (* Harvey P. Dale, Apr 27 2016 *)

Formula

a(n) = 3^n + (-1)^n - 0^n.

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

E.g.f.: exp(3*x)-exp(0)+exp(-x).

a(n) = 2 * A046717(n) for n >= 1.