A097637 a(n) = Fibonacci(floor(n/16) + BinaryWeight(n mod 16)).

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, 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, 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

Offset

0,8

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

a(n) = a(n-16) + a(n-32). - Andrew Howroyd, Dec 14 2025

Mathematica

M={{0, 1}, {1, 1}};
A[0]:={{0, 1}, {1, 1}};
A[1]=M.A[0]
A[2]=M.A[1]
AA[0]:={{A[0], A[1]}, {A[1], A[2]}}
MatrixForm[M.AA[0]]
MatrixForm[AA[0]]
a=Flatten[Table[MatrixPower[M, n].AA[0], {n, 0, 12}]]
Dimensions[a]

Prog

(PARI) a(n)=fibonacci(n\16 + hammingweight(n%16)); \\ Andrew Howroyd, May 16 2021

Crossrefs

Cf. A000045, A000120.

Sequence in context: A058761 A050119 A290253 * A161094 A307343 A340034

Adjacent sequences: A097634 A097635 A097636 * A097638 A097639 A097640

Keyword

nonn,easy,less,dumb

Author

Roger L. Bagula, Sep 20 2004

Extensions

New name and edited, Joerg Arndt, May 16 2021

Status

approved