%I M0730 N0273 #36 Apr 13 2022 13:25:16
%S 2,3,5,11,16,38,54,130,184,444,628,1516,2144,5176,7320,17672,24992,
%T 60336,85328,206000,291328,703328,994656,2401312,3395968,8198592,
%U 11594560,27991744,39586304,95569792,135156096,326295680,461451776,1114043136,1575494912
%N a(2n) = a(2n-1) + 2a(2n-2), a(2n+1) = a(2n) + a(2n-1), with a(1) = 2 and a(2) = 3.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001882/b001882.txt">Table of n, a(n) for n = 1..500</a>
%H Michael Fried et al., <a href="https://www.jstor.org/stable/2313357">Problem E1738</a>, Amer. Math. Monthly, 72 (1965), 1024-1025.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4, 0, -2).
%F G.f.: see Maple program.
%p A001882:=-(-2-3*z+3*z**2+z**3)/(1-4*z**2+2*z**4); # [_Simon Plouffe_ in his 1992 dissertation for offset 0.]
%t a[1] = 2; a[2] = 3; a[n_] := a[n] = If[EvenQ[n], a[n-1] + 2*a[n-2], a[n-1] + a[n-2]]; Table[a[n], {n, 50}] (* _T. D. Noe_, Aug 10 2012 *)
%o (PARI) x='x+O('x^50); Vec((2+3*x-3*x^2-x^3)/(1-4*x^2+2*x^4)) \\ _G. C. Greubel_, Aug 13 2017
%Y Cf. A161941 (bisection).
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Removed the attribute "conjectured" from the Plouffe g.f. _R. J. Mathar_, Aug 17 2009