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A166138 Trisection A022998(3n+1).

%I A166138 #18 Apr 28 2016 11:24:02
%S A166138 1,8,7,20,13,32,19,44,25,56,31,68,37,80,43,92,49,104,55,116,61,128,67,
%T A166138 140,73,152,79,164,85,176,91,188,97,200,103,212,109,224,115,236,121,
%U A166138 248,127,260,133,272,139,284,145,296,151,308,157,320,163,332,169,344,175,356,181,368,187,380,193,392
%N A166138 Trisection A022998(3n+1).
%H A166138 G. C. Greubel, <a href="/A166138/b166138.txt">Table of n, a(n) for n = 0..5000</a>
%H A166138 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A166138 a(2n) = 6n+1 = A016921(n).
%F A166138 a(2n+1) = 12n+8 = A017617(n).
%F A166138 a(n) = 2*a(n-2)-a(n-4) = (3n+1)*(3-(-1)^n)/2.
%F A166138 From _G. C. Greubel_, Apr 26 2016: (Start)
%F A166138 O.g.f.: (1 + 8*x + 5*x^2 + 4*x^3)/((1 - x)^2*(1 + x)^2).
%F A166138 E.g.f.: (1/2)*(-1 + 3*x + (3+9*x)*exp(2*x))*exp(-x). (End)
%t A166138 LinearRecurrence[{0,2,0,-1},{1,8,7,20},70] (* _Harvey P. Dale_, Aug 15 2012 *)
%t A166138 Table[If[OddQ@ #, #, 2 #] &[3 n + 1], {n, 0, 65}] (* or *)
%t A166138 CoefficientList[Series[(1 + 8 x + 5 x^2 + 4 x^3)/((1 - x)^2 (1 + x)^2), {x, 0, 65}], x] (* _Michael De Vlieger_, Apr 27 2016 *)
%Y A166138 Cf. A165988, A166304.
%K A166138 nonn,easy
%O A166138 0,2
%A A166138 _Paul Curtz_, Oct 08 2009