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A bisection of A002083.
2

%I #14 Mar 08 2022 16:47:51

%S 1,1,3,11,42,165,654,2605,10398,41550,166116,664299,2656866,10626810,

%T 42505932,170021123,680079282,2720306730,10881206124,43524782946,

%U 174099048684,696396028620,2785583782248,11142334464693,44569336530174,178277343463830,713109368541588

%N A bisection of A002083.

%D H. Brocard, Query 4293, L'Intermédiaire des Mathématiciens, 23 (1916), 58-59. - _N. J. A. Sloane_, Mar 08 2022

%F a(0)=a(1)=1; a(2)=3; a(n) = 4*a(n-1) + ((-1)^(n-1)-3)/2 * a(floor((n-1)/2)). - _Carl R. White_, Oct 06 2017

%p A259858 := proc(n)

%p A002083(2*n+1) ;

%p end proc:

%p seq(A259858(n),n=0..30) ; # _R. J. Mathar_, Jul 09 2015

%t a[n_] := a[n] = If[n < 3, 1 + 2 Boole@ PrimeQ@ n, 4 a[n - 1] + ((-1)^(n - 1) - 3)/2*a[Floor[(n - 1)/2]]]; Array[a, 27, 0] (* _Michael De Vlieger_, Oct 06 2017 *)

%Y Cf. A002083, A245094.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 07 2015