A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Michael Gilleland, Some Self-Similar Integer Sequences
• R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A011662.

Cf. A011747..A011751 for similar sequences and A011655 - A011745 for other binary m-sequences.

Programs

Maple

series((1+x^2)/(1+x^2+x^5),x,100) mod 2;

Mathematica

Mod[CoefficientList[Series[(1+x^2)/(1+x^2+x^5),{x,0,80}],x],2] (* Harvey P. Dale, Jul 19 2023 *)

PARI

A011746_vec=Vec((1+x^2)/(1+x^2+x^5)+O(x^31))%2 \\ For illustrative purpose.
A011746(n)=bittest(377253537,n%31) \\ M. F. Hasler, Feb 17 2018

Formula

a(n) = A088002(n) mod 2. - R. J. Mathar, May 26 2008

G.f.: (1+x^5+x^7+x^9+x^10+x^11+x^13+x^14+x^18+x^19+x^20+x^21+x^22+x^25+x^26+x^28)/(1-x^31). - Robert Israel, May 06 2018

a(n) = A011662(n-1). - R. J. Mathar, Jan 12 2024