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

0,1

Links

Table of n, a(n) for n=0..80.

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A011662.

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

Sequence in context: A354927 A173861 A359464 * A071005 A287801 A089510

Adjacent sequences: A011743 A011744 A011745 * A011747 A011748 A011749

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved