OFFSET
2,3
REFERENCES
Marc LeBrun, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..8191
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, pp. 6, 24, 38-39, 64.
M. Le Brun, Email to N. J. A. Sloane, Jul 1991
FORMULA
G.f.: 1/(1-x)^2 * Sum_{k>=0} 2^k*t^2/(1+t)^2, t = x^2^k. - Ralf Stephan, Feb 12 2003
a(0) = a(1) = 0, a(2n) = 2*a(n-1) + 2*a(n) + n, a(2n+1) = 4*a(n).
a(n) = 2*(Sum_{k=1..floor((n-1)/2)} k AND n-k) + m where m = 0 if n is odd and n/2 otherwise. - Chai Wah Wu, May 07 2023
MATHEMATICA
Array[Sum[BitAnd[k, # - k], {k, # - 1}] &, 60, 2] (* Michael De Vlieger, Oct 27 2022 *)
PROG
(Python)
def A006581(n): return (sum(k&n-k for k in range(1, n+1>>1))<<1)+(0 if n&1 else n>>1) # Chai Wah Wu, May 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved