A011731 A binary m-sequence: expansion of reciprocal of x^18 + x^7 + 1 (mod 2, shifted by 17 initial 0's).

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

Offset

0,1

Comments

Periodic with period of length 2^18 - 1 = 262143. - 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.

Index entries for linear recurrences with constant coefficients, order 262143.

Formula

G.f. = x^17/(x^18 + x^7 + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Prog

(PARI) A=matrix(N=18, N, i, j, if(i>1, i==j+1, setsearch([7, N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[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: A185709 A011732 A353473 * A085980 A023974 A277164

Adjacent sequences: A011728 A011729 A011730 * A011732 A011733 A011734

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved