A048297 Coefficients in power series expansion over GF(2)[ X^(-1) ] of continued fraction [ 0, X, X^2, X^4, X^8, X^16, ... ].

1, 4, 7, 13, 16, 25, 28, 31, 49, 52, 55, 61, 64, 97, 100, 103, 109, 112, 121, 124, 127, 193, 196, 199, 205, 208, 217, 220, 223, 241, 244, 247, 253, 256, 385, 388, 391, 397, 400, 409, 412, 415, 433, 436, 439, 445, 448, 481, 484, 487, 493, 496, 505

Offset: 0

Author

Jeffrey Shallit

Keywords

• nonn

References

• M. Morii and M. Kasahara, Perfect staircase profile of linear complexity for finite sequences, Info. Proc. Letters 44 (1992), 85-89, esp. p. 88.

Crossrefs

Cf. A003714 (Fibbinary numbers).

Formula

n is in the sequence iff 2n-1 is in iff 4n is in [and a(0)=1]. So a(Fib(n)) = 2^n if n is even and a(Fib(n)) = 2^n-1 if n is odd. - Henry Bottomley, Sep 25 2000

a(n) = 3*A003714(n)+1. - T. D. Noe, Dec 20 2006