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

0,2

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

Table of n, a(n) for n=0..27.

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

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.

Mathematica

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

Crossrefs

Except for leading term, same as A102345.

Cf. A046717, A111317.

Sequence in context: A183331 A324914 A025589 * A321240 A322201 A099583

Adjacent sequences: A084179 A084180 A084181 * A084183 A084184 A084185

Keyword

easy,nonn

Author

Paul Barry, May 19 2003

Status

approved