A193652 A020988 and A007583 interleaved.

0, 1, 2, 3, 10, 11, 42, 43, 170, 171, 682, 683, 2730, 2731, 10922, 10923, 43690, 43691, 174762, 174763, 699050, 699051, 2796202, 2796203, 11184810, 11184811, 44739242, 44739243, 178956970, 178956971, 715827882, 715827883, 2863311530, 2863311531, 11453246122

Offset: 0

Author

Reinhard Zumkeller, Aug 08 2011

Keywords

• nonn
• easy

Comments

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

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

Links

• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

Programs

Maple

A193652 := proc(n)
        if type (n,'even') then
                A020988(n/2) ;
        else
                A007583(floor(n/2)) ;
        end if;
end proc: # R. J. Mathar, Jul 20 2016

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {0, 1, 2, 3}, 35] (* Jean-François Alcover, Dec 16 2021 *)

Formula

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

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

Extensions

Terms corrected by R. J. Mathar, Feb 19 2015