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
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
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Jul 22 2003
STATUS
approved