A085765 Partial sums and bisection of A086450.

1, 2, 4, 5, 9, 11, 16, 17, 26, 30, 41, 43, 59, 64, 81, 82, 108, 117, 147, 151, 192, 203, 246, 248, 307, 323, 387, 392, 473, 490, 572, 573, 681, 707, 824, 833, 980, 1010, 1161, 1165, 1357, 1398, 1601, 1612, 1858, 1901, 2149, 2151, 2458, 2517

Offset

0,2

Comments

Sum of inverses of a(n) is 1.5398789314089581123...

Conjecture: log(a(n))/log(n) grows unboundedly.

Conjecture: a(n) mod 2 repeats the 7-pattern 0,0,1,1,1,0,1.

The conjecture concerning the mod 2 pattern follows directly from the corresponding conjecture proved in A086450. - Lambert Herrgesell (zero815(AT)googlemail.com), May 08 2007

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = A086450(2n) = A086450(0) + ... + A086450(n). - Charles R Greathouse IV, Sep 26 2013

Maple

b:= proc(n) local m; b(n):= `if`(n=0, 1,
      `if`(irem(n, 2, 'm')=1, b(m), a(m)))
    end:
a:= proc(n) a(n):= b(n) +`if`(n=0, 0, a(n-1)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 26 2013

Mathematica

b[0] = 1;
b[n_] := b[n] = If[EvenQ[n], Sum[b[n/2-k], {k, 0, n/2}], b[(n-1)/2]]; A085765 = Table[b[n], {n, 0, 100}] // Accumulate (* Jean-François Alcover, Mar 28 2017 *)

Prog

(PARI) v=vector(1000); v[1]=1; s=1; for(n=2, 1000, v[n]=if(n%2==0, v[n/2], s=s+v[(n+1)/2]; print1(s", "); s))
(PARI) lista(nn) = {v=vector(nn); v[1]=1; s=1; for(n = 2, nn, v[n]= if(n%2==0, v[n/2], s=s+v[(n+1)/2])); forstep(i = 1, nn, 2, print1(v[i], ", "); ); } \\ Michel Marcus, Sep 26 2013

Crossrefs

Sequence in context: A258652 A065514 A152186 * A211521 A039871 A365042

Adjacent sequences: A085762 A085763 A085764 * A085766 A085767 A085768

Keyword

nonn,easy

Author

Ralf Stephan, Jul 22 2003

Status

approved