A280261 Period 12 sequence [0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, ...].

0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1

Offset

0

Links

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

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

Formula

a(n) = (-1)^(n-1)*a(n-1) + a(n-2) with a(0) = 0 and a(1) = 1.

a(n) = A260192(n+1) = A117441(n+2) = A260190(n+4).

G.f.: x * (1 - x - x^2) / (1 - x^2 + x^4).

Example

G.f. = x - x^2 - x^4 - x^5 - x^7 + x^8 + x^10 + x^11 + ...

Mathematica

PadRight[{}, 100, {0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1}] (* Vincenzo Librandi, Dec 31 2016 *)
LinearRecurrence[{0, 1, 0, -1}, {0, 1, -1, 0}, 100] (* Harvey P. Dale, Feb 15 2017 *)

Prog

(Ruby)
def A(m, n)
  i, a, b = 0, 0, 1
  ary = [0]
  while i < n
    i += 1
    a, b = b, b * m ** i + a
    ary << a
  end
  ary
end
def A280261(n)
  A(-1, n)
end
(Magma) &cat [[0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1]^^10]; // Vincenzo Librandi, Dec 31 2016

Crossrefs

Cf. A117441, A260190, A260192.

Cf. similar sequences with the recurrence q^(n-1)*a(n-1) + a(n-2) for n>1, a(0)=0 and a(1)=1: A280222 (q=-3), A280221 (q=-2), this sequence (q=-1), A000045 (q=1), A015473 (q=2), A015474 (q=3), A015475 (q=4), A015476 (q=5), A015477 (q=6), A015479 (q=7), A015480 (q=8), A015481 (q=9), A015482 (q=10), A015484 (q=11).

Sequence in context: A181932 A284792 A094217 * A174784 A092220 A011655

Adjacent sequences: A280258 A280259 A280260 * A280262 A280263 A280264

Keyword

sign,easy

Author

Seiichi Manyama, Dec 30 2016

Status

approved