A084182 - OEIS

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

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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