A011744 A binary m-sequence: expansion of reciprocal of x^31 + x^3 + 1 (mod 2, shifted by 30 initial 0's).

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

Offset

0,1

Comments

Periodic with period 2^31-1 = 2147483647. - M. F. Hasler, Feb 17 2018

References

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.

H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

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

Mathematica

Join[Table[0, 30], Mod[CoefficientList[1/(x^31+x^3+1) + O[x]^52, x], 2]] (* Jean-François Alcover, Feb 23 2018 *)

Prog

(PARI) A011744_vec=concat([1..31]*0, Vec(1/(x^32+x^28+x^27+x+1)+O(x^99))%2)
A=matrix(31, 31, i, j, if(i>1, i==j+1, setsearch([3, 31], j)>0))*Mod(1, 2);
A011744(n)=lift((A^(n-30))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Sequence in context: A304572 A070204 A011745 * A358754 A354996 A351539

Adjacent sequences: A011741 A011742 A011743 * A011745 A011746 A011747

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved