A011751 Expansion of (1 + x^4)/(1 + x + x^3 + x^4 + x^5) mod 2.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• 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), i.e., 31-periodic.

Crossrefs

Cf. A011655..A011750 for other binary m-sequences.

Programs

Maple

series((1+x^4)/(1+x+x^3+x^4+x^5),x,100) mod 2;
[seq(coeff(series((1+x^4)/(1+x+x^3+x^4+x^5),x,100) mod 2,x,n),n=0..80)]; # Muniru A Asiru, Feb 18 2018
A011751 := n -> coeftayl((1+x^4)/(1+x+x^3+x^4+x^5),x=0,n) mod 2 # M. F. Hasler, Feb 18 2018

Mathematica

Mod[ CoefficientList[ Series[(1 + x^4)/(1 + x + x^3 + x^4 + x^5), {x, 0, 105}], x], 2] (* Robert G. Wilson v, Feb 19 2018 *)

PARI

a(n)=bittest(1826728215,n%31) \\ M. F. Hasler, Feb 17 2018

Formula

a(n+31) = a(n) for all n. - M. F. Hasler, Feb 17 2018