A086845 a(1) = 0, a(n) = a(floor(n/2)) + 2*a(ceiling(n/2)) + floor(n/2).

0, 1, 3, 5, 9, 12, 16, 19, 27, 32, 38, 42, 50, 55, 61, 65, 81, 90, 100, 106, 118, 125, 133, 138, 154, 163, 173, 179, 191, 198, 206, 211, 243, 260, 278, 288, 308, 319, 331, 338, 362, 375, 389, 397, 413, 422, 432, 438, 470, 487, 505, 515, 535

Offset: 1

Author

Ralf Stephan, Aug 09 2003

Keywords

• nonn
• easy

Comments

Number of comparators used in Bose-Nelson networks.

Conjecture: partial sums of A087808. - Sean A. Irvine, Jul 14 2022

Links

• R. C. Bose and R. J. Nelson, A sorting problem, J. Assoc. Comput. Mach. 9 (1962), 282-296.
• P. J. Grabner and H.-K. Hwang, Digital sums and divide-and-conquer recurrences: Fourier expansions and absolute convergence, Constructive Approximation, Jan. 2005, Volume 21, Issue 2, pp 149-179.

Crossrefs

Cf. A064194.

Programs

Magma

[n le 1 select 0 else Self(Floor(n/2)) + 2*Self(Ceiling(n/2)) + Floor(n/2): n in [1..60]]; // Vincenzo Librandi, Aug 30 2016

PARI

a(n)=if(n<2,0,a(floor(n/2))+2*a(ceil(n/2))+floor(n/2))