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%I #29 Nov 19 2023 21:17:00
%S 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,
%T -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,
%U 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
%N Period 12 sequence [0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, ...].
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1).
%F a(n) = (-1)^(n-1)*a(n-1) + a(n-2) with a(0) = 0 and a(1) = 1.
%F a(n) = A260192(n+1) = A117441(n+2) = A260190(n+4).
%F G.f.: x * (1 - x - x^2) / (1 - x^2 + x^4).
%e G.f. = x - x^2 - x^4 - x^5 - x^7 + x^8 + x^10 + x^11 + ...
%t PadRight[{}, 100, {0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1}] (* _Vincenzo Librandi_, Dec 31 2016 *)
%t LinearRecurrence[{0,1,0,-1},{0,1,-1,0},100] (* _Harvey P. Dale_, Feb 15 2017 *)
%o (Ruby)
%o def A(m, n)
%o i, a, b = 0, 0, 1
%o ary = [0]
%o while i < n
%o i += 1
%o a, b = b, b * m ** i + a
%o ary << a
%o end
%o ary
%o end
%o def A280261(n)
%o A(-1, n)
%o end
%o (Magma) &cat [[0,1,-1,0,-1,-1,0,-1,1,0,1,1]^^10]; // _Vincenzo Librandi_, Dec 31 2016
%Y Cf. A117441, A260190, A260192.
%Y 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).
%K sign,easy
%O 0
%A _Seiichi Manyama_, Dec 30 2016
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