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%I #19 Dec 19 2023 18:15:41
%S 1,2,10,26,82,242,730,2186,6562,19682,59050,177146,531442,1594322,
%T 4782970,14348906,43046722,129140162,387420490,1162261466,3486784402,
%U 10460353202,31381059610,94143178826,282429536482,847288609442,2541865828330,7625597484986
%N a(n) = 3^n + (-1)^n - [1/(n+1)], where [] represents the floor function.
%C Binomial transform of A084181.
%C From _Peter Bala_, Dec 26 2012: (Start)
%C 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.
%C (End)
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F a(n) = 3^n + (-1)^n - 0^n.
%F G.f.: (1+3*x^2)/((1+x)*(1-3*x)).
%F E.g.f.: exp(3*x)-exp(0)+exp(-x).
%F a(n) = 2 * A046717(n) for n >= 1.
%t LinearRecurrence[{2,3},{1,2,10},30] (* _Harvey P. Dale_, Apr 27 2016 *)
%Y Except for leading term, same as A102345.
%Y Cf. A046717, A111317.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 19 2003