A280261 - OEIS

%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