A097637 - OEIS

%I #18 May 16 2021 08:02:38

%S 0,1,1,1,1,1,1,2,1,1,1,2,1,2,2,3,1,1,1,2,1,2,2,3,1,2,2,3,2,3,3,5,1,2,

%T 2,3,2,3,3,5,2,3,3,5,3,5,5,8,2,3,3,5,3,5,5,8,3,5,5,8,5,8,8,13,3,5,5,8,

%U 5,8,8,13,5,8,8,13,8,13,13,21,5,8,8,13,8,13,13,21,8,13,13,21,13,21,21,34,8

%N a(n) = Fibonacci(floor(n/16) + BinaryWeight(n mod 16)).

%t M={{0, 1}, {1, 1}};

%t A[0]:={{0, 1}, {1, 1}};

%t A[1]=M.A[0]

%t A[2]=M.A[1]

%t AA[0]:={{A[0], A[1]}, {A[1], A[2]}}

%t MatrixForm[M.AA[0]]

%t MatrixForm[AA[0]]

%t a=Flatten[Table[MatrixPower[M, n].AA[0], {n, 0, 12}]]

%t Dimensions[a]

%o (PARI) a(n)=fibonacci(n\16 + hammingweight(n%16)); \\ _Andrew Howroyd_, May 16 2021

%Y Cf. A000045, A000120.

%K nonn,easy,less,dumb

%O 0,8

%A _Roger L. Bagula_, Sep 20 2004

%E New name and edited, _Joerg Arndt_, May 16 2021