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

0,3

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

Table of n, a(n) for n=0..34.

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

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

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 *)

Crossrefs

Sequence in context: A307034 A081868 A212103 * A345369 A092986 A295577

Adjacent sequences: A193649 A193650 A193651 * A193653 A193654 A193655

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 08 2011

Extensions

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

Status

approved