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A132162 a(2n+1) = 3*a(2*n) - 4*n with a(0) = 1, a(1) = 3.

%I A132162 #20 Jul 05 2020 10:59:40
%S A132162 1,3,5,11,7,13,9,15,17,35,19,37,21,39,23,41,25,43,27,45,29,47,31,49,
%T A132162 33,51,53,107,55,109,57,111,59,113,61,115,63,117,65,119,67,121,69,123,
%U A132162 71,125,73,127,75,129,77,131,79,133,81,135,83,137,85,139,87,141,89,143,91
%N A132162 a(2n+1) = 3*a(2*n) - 4*n with a(0) = 1, a(1) = 3.
%H A132162 Robert Israel, <a href="/A132162/b132162.txt">Table of n, a(n) for n = 0..10000</a>
%F A132162 Note (a(2*n+1)-a(2*n))/2 gives A132171.
%F A132162 From _Robert Israel_, Feb 24 2017: (Start)
%F A132162 a(2*n) = 2*n + A132171(n) = 2*n + 3^floor(log[3](2*n+1)).
%F A132162 a(2*n+1) = 2*n + 3*A132171(n) = 2*n + 3*3^floor(log[3](2*n+1)).
%F A132162 a(6*n+2) = 4*n+2+a(2*n+1).
%F A132162 a(6*n+3) = 2+3*a(2*n+1).
%F A132162 a(6*n+4) = 4*n+4+a(2*n+1).
%F A132162 a(6*n+5) = 4+3*a(2*n+1).
%F A132162 a(6*n+6) = 4*n+6+a(2*n+1).
%F A132162 a(6*n+7) = 6+3*a(2*n+1).
%F A132162 (End)
%p A132162 f:= proc(n) option remember; local j;
%p A132162 j:= (n-2) mod 6 + 2;
%p A132162 if n::odd then j-1 + 3*procname(1+(n-j)/3)
%p A132162 else (2*n+j)/3 + procname(1+(n-j)/3)
%p A132162   fi
%p A132162 end proc:
%p A132162 f(0):= 1: f(1):= 3:
%p A132162 map(f, [$0..100]); # _Robert Israel_, Feb 24 2017
%t A132162 f[n_] := f[n] = With[{j = Mod[n-2, 6]+2}, If[OddQ[n], j-1 + 3*f[1+(n-j)/3], (2n+j)/3 + f[1+(n-j)/3]]];
%t A132162 f[0] = 1; f[1] = 3;
%t A132162 f /@ Range[0, 100] (* _Jean-François Alcover_, Jun 22 2020, after Maple *)
%Y A132162 Cf. A132171.
%K A132162 nonn,look
%O A132162 0,2
%A A132162 _Paul Curtz_, Nov 04 2007