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A085765 Partial sums and bisection of A086450.

%I A085765 #21 Mar 28 2017 14:55:19
%S A085765 1,2,4,5,9,11,16,17,26,30,41,43,59,64,81,82,108,117,147,151,192,203,
%T A085765 246,248,307,323,387,392,473,490,572,573,681,707,824,833,980,1010,
%U A085765 1161,1165,1357,1398,1601,1612,1858,1901,2149,2151,2458,2517
%N A085765 Partial sums and bisection of A086450.
%C A085765 Sum of inverses of a(n) is 1.5398789314089581123...
%C A085765 Conjecture: log(a(n))/log(n) grows unboundedly.
%C A085765 Conjecture: a(n) mod 2 repeats the 7-pattern 0,0,1,1,1,0,1.
%C A085765 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
%H A085765 Alois P. Heinz, <a href="/A085765/b085765.txt">Table of n, a(n) for n = 0..10000</a>
%F A085765 a(n) = A086450(2n) = A086450(0) + ... + A086450(n). - _Charles R Greathouse IV_, Sep 26 2013
%p A085765 b:= proc(n) local m; b(n):= `if`(n=0, 1,
%p A085765       `if`(irem(n, 2, 'm')=1, b(m), a(m)))
%p A085765     end:
%p A085765 a:= proc(n) a(n):= b(n) +`if`(n=0, 0, a(n-1)) end:
%p A085765 seq(a(n), n=0..100);  # _Alois P. Heinz_, Sep 26 2013
%t A085765 b[0] = 1;
%t A085765 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 *)
%o A085765 (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))
%o A085765 (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
%K A085765 nonn,easy
%O A085765 0,2
%A A085765 _Ralf Stephan_, Jul 22 2003