A067148 Fibonacci-like sequences. a(n) is the number of pairs of integers (n,i), 02, of a sequence {b(k)} satisfying b(1)=1, b(2)>0 and b(k)=b(k-1)+b(k-2) for all k>2.

0, 1, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 4, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 2, 3, 1, 3, 3, 2, 1, 3, 1, 3, 2, 3, 1, 4, 2, 2, 2, 2, 1, 5, 1, 3, 2, 2, 2, 3, 2, 3, 2, 3, 1, 3, 1, 2, 3, 3, 1, 3, 1, 4, 2, 2, 2, 4, 2, 2, 2, 2, 1, 4, 1, 3, 3, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 3, 1, 4, 1, 3, 2, 2

Offset: 1

Author

John W. Layman, Jan 04 2002

Keywords

• nonn

Crossrefs

Cf. A067149 gives the indices of records. See A067150 for a variation.

Programs

Mathematica

a[ n_ ] := Module[ {}, If[ n==2, Return[ 1 ] ]; For[ f0=3; f1=2; f2=1; c=0, f0<=n, f0=(f2=f1)+(f1=f0), If[ Mod[ n-f0, f2 ]==0, c++ ] ]; c ]

Extensions

Edited by Dean Hickerson, Jan 17 2002