A304577 Period 21: repeat (0,0,0,0,1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1).

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

Offset

0

Links

Table of n, a(n) for n=0..83.

Michael R. Bush and Danjoseph Quijada, Period sets of linear recurrence over finite fields and related commutative rings, arXiv:1805.03238 [math.NT], 2018 (see Remark 3.7, page 13).

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: x^4*(1+x+x^2+x^3+x^4+x^6+x^8+x^11+x^12+x^16)/(1-x^21).

a(n) = a(n-21) for n >= 21.

Mathematica

CoefficientList[Series[(x^4 (1 + x + x^2 + x^3 + x^4 + x^6 + x^8 + x^11 + x^12 + x^16))/(1 - x^21), {x, 0, 100}], x]
PadRight[{}, 120, {0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1}] (* Harvey P. Dale, Oct 13 2020 *)

Prog

(Magma) &cat[[0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]^^4];

Crossrefs

Sequence in context: A011663 A091247 A085137 * A194670 A130543 A185013

Adjacent sequences: A304574 A304575 A304576 * A304578 A304579 A304580

Keyword

nonn,easy

Author

Vincenzo Librandi, May 15 2018

Status

approved