A083662 - OEIS

%I #12 Jun 20 2018 01:32:49

%S 1,2,3,3,5,5,5,5,8,8,8,8,8,8,8,8,13,13,13,13,13,13,13,13,13,13,13,13,

%T 13,13,13,13,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,

%U 21,21,21,21,21,21,21,21,21,21,21,21,21,34,34,34,34,34,34,34,34,34,34,34

%N a(n) = a(floor(n/2)) + a(floor(n/4)), n > 0; a(0)=1.

%C A000045(n+2) = a(A131577(n))and A000045(m+2) < a(m) for m < A131577(n). - _Reinhard Zumkeller_, Sep 26 2009

%H R. Zumkeller, <a href="/A083662/b083662.txt">Table of n, a(n) for n = 0..10000</a>

%F For n > 0, a(n) = F([log(n)/log(2)]+3) where F(k) denotes the k-th Fibonacci number. For n >= 3, F(n) appears 2^(n-3) times. More generally, if p is an integer > 1 and a(n) = a(floor(n/p)) + a(floor(n/p^2)), n > 0, a(0)=1, then for n > 0, a(n) = F(floor(log(n)/log(p)) + 3).

%o (PARI) a(n)=if(n<1,n==0,a(n\2)+a(n\4))

%Y Cf. A088468.

%Y A007731, A165704, A165706. - _Reinhard Zumkeller_, Sep 26 2009

%K nonn

%O 0,2

%A _Benoit Cloitre_, Oct 05 2003