OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
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. 34, 37, 41.
Ralf Stephan, Some divide-and-conquer sequences ...
Ralf Stephan, Table of generating functions
FORMULA
a(n) = b(n+1), with b(2n) = 2*b(n)+2*b(n-1)+1, b(2n+1) = 4*b(n)+1.
a(n) = (n+2)*2^k - (2*4^k + 1)/3 where k = floor(log_2(n+2)) = A000523(n+2). - Kevin Ryde, Nov 27 2020
MAPLE
a:= proc(n) option remember; `if`(n<0, 0, 1+
(t-> 2*(a(floor(t))+a(ceil(t))))(n/2-1))
end:
seq(a(n), n=0..55); # Alois P. Heinz, Jul 10 2019
MATHEMATICA
b[n_] := b[n] = If[EvenQ[n], 2 b[n/2] + 2 b[n/2-1] + 1, 4 b[(n-1)/2] + 1];
b[1] = 1; b[2] = 3;
a[n_] := b[n+1];
a /@ Range[0, 55] (* Jean-François Alcover, Nov 02 2020 *)
PROG
(PARI) a(n) = n+=2; my(k=logint(n, 2)); n<<k - (2<<(2*k))\/3; \\ Kevin Ryde, Nov 27 2020
CROSSREFS
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Sep 01 2001
EXTENSIONS
More terms from Ralf Stephan, Sep 15 2003
STATUS
approved