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A193652 A020988 and A007583 interleaved.

%I A193652 #26 Dec 16 2021 11:49:11
%S A193652 0,1,2,3,10,11,42,43,170,171,682,683,2730,2731,10922,10923,43690,
%T A193652 43691,174762,174763,699050,699051,2796202,2796203,11184810,11184811,
%U A193652 44739242,44739243,178956970,178956971,715827882,715827883,2863311530,2863311531,11453246122
%N A193652 A020988 and A007583 interleaved.
%C A193652 a(2*n) = A020988(n), a(2*n+1) = a(2*n) + 1 = A007583(n);
%C A193652 apart from initial zero, record values in A048985: a(n)=A048985(A029744(n)) and a(n)<A048985(m) for m<A029744(n).
%H A193652 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).
%F A193652 a(n) = 2 * (4^floor(n/2) - 1) / 3 + n mod 2.
%F A193652 G.f.: ( -x*(-1-2*x+2*x^2) ) / ( (x-1)*(2*x+1)*(2*x-1)*(1+x) ). - _R. J. Mathar_, Feb 19 2015
%p A193652 A193652 := proc(n)
%p A193652         if type (n,'even') then
%p A193652                 A020988(n/2) ;
%p A193652         else
%p A193652                 A007583(floor(n/2)) ;
%p A193652         end if;
%p A193652 end proc: # _R. J. Mathar_, Jul 20 2016
%t A193652 LinearRecurrence[{0, 5, 0, -4}, {0, 1, 2, 3}, 35] (* _Jean-François Alcover_, Dec 16 2021 *)
%K A193652 nonn,easy
%O A193652 0,3
%A A193652 _Reinhard Zumkeller_, Aug 08 2011
%E A193652 Terms corrected by _R. J. Mathar_, Feb 19 2015