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 A084182 a(n) = 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, 2541865828330, 7625597484986 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)