A011738 A binary m-sequence: expansion of reciprocal of x^25 + x^3 + 1 (mod 2, shifted by 24 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, 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, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0

Offset

0,1

Comments

Sequence is 2^25-1 = 33554431-periodic. - 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

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, order 33554431.

Index entries for periodic sequences with large period.

Formula

G.f. = x^24/(x^25+x^3+1), over GF(2). - M. F. Hasler, Feb 17 2018

Maple

N:= 200: # to get a(0)..a(N)
A:= Array(0..N):
A[24]:= 1:
for n from 25 to N do A[n]:= A[n-3] + A[n-25] mod 2 od:
convert(A, list); # Robert Israel, Mar 25 2018

Prog

(PARI) A=matrix(N=25, N, i, j, if(i>1, i==j+1, setsearch([3, N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Crossrefs

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

Sequence in context: A305821 A305892 A324870 * A011737 A011736 A085982

Adjacent sequences: A011735 A011736 A011737 * A011739 A011740 A011741

Keyword

nonn

Author

N. J. A. Sloane

Status

approved