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A084182 3^n+(-1)^n-[1/(n+1)], where [] represents the floor function. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A084181. a(n)/2=A046717(n), n>0.

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..25.

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).

MATHEMATICA

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

CROSSREFS

Except for leading term, same as A102345.

Cf. 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

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Last modified January 26 11:20 EST 2020. Contains 331279 sequences. (Running on oeis4.)