A083662 a(n) = a(floor(n/2)) + a(floor(n/4)), n > 0; a(0)=1.

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, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34

Offset: 0

Author

Benoit Cloitre, Oct 05 2003

Keywords

• nonn

Comments

A000045(n+2) = a(A131577(n))and A000045(m+2) < a(m) for m < A131577(n). - Reinhard Zumkeller, Sep 26 2009

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A088468.

A007731, A165704, A165706. - Reinhard Zumkeller, Sep 26 2009

Programs

PARI

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

Formula

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).