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A020988 and A007583 interleaved.
7

%I #26 Dec 16 2021 11:49:11

%S 0,1,2,3,10,11,42,43,170,171,682,683,2730,2731,10922,10923,43690,

%T 43691,174762,174763,699050,699051,2796202,2796203,11184810,11184811,

%U 44739242,44739243,178956970,178956971,715827882,715827883,2863311530,2863311531,11453246122

%N A020988 and A007583 interleaved.

%C a(2*n) = A020988(n), a(2*n+1) = a(2*n) + 1 = A007583(n);

%C apart from initial zero, record values in A048985: a(n)=A048985(A029744(n)) and a(n)<A048985(m) for m<A029744(n).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).

%F a(n) = 2 * (4^floor(n/2) - 1) / 3 + n mod 2.

%F 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 := proc(n)

%p if type (n,'even') then

%p A020988(n/2) ;

%p else

%p A007583(floor(n/2)) ;

%p end if;

%p end proc: # _R. J. Mathar_, Jul 20 2016

%t LinearRecurrence[{0, 5, 0, -4}, {0, 1, 2, 3}, 35] (* _Jean-François Alcover_, Dec 16 2021 *)

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Aug 08 2011

%E Terms corrected by _R. J. Mathar_, Feb 19 2015