A259858 A bisection of A002083.

1, 1, 3, 11, 42, 165, 654, 2605, 10398, 41550, 166116, 664299, 2656866, 10626810, 42505932, 170021123, 680079282, 2720306730, 10881206124, 43524782946, 174099048684, 696396028620, 2785583782248, 11142334464693, 44569336530174, 178277343463830, 713109368541588

Offset: 0

Author

N. J. A. Sloane, Jul 07 2015

Keywords

• nonn

References

• H. Brocard, Query 4293, L'Intermédiaire des Mathématiciens, 23 (1916), 58-59. - N. J. A. Sloane, Mar 08 2022

Crossrefs

Cf. A002083, A245094.

Programs

Maple

A259858 := proc(n)
    A002083(2*n+1) ;
end proc:
seq(A259858(n),n=0..30) ; # R. J. Mathar, Jul 09 2015

Mathematica

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 *)

Formula

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