A278718 Numerators of A189733: periodic sequence repeating [0, 1, 1, 1, 0, -1].

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

Offset

0

Comments

See A189733.

Links

Table of n, a(n) for n=0..100.

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

Formula

G.f.: x*(1+x^2-x^3)/((1-x)*(1-x+x^2)*(1+x+x^2)).

From Wesley Ivan Hurt, Oct 03 2017: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n > 4.

a(n) = (1+(-1)^floor((n-1)/3))/2-floor((n+1)/6)+floor(n/6). (End)

Mathematica

b[m_, n_] := b[m, n] = Which[m == n, 0, n == m + 1, (-1)^(n + 1)/n, n > m, b[m, n - 1] + b[m + 1, n - 1], n < m, b[m - 1, n + 1] - b[m - 1, n]]; a[n_] := b[0, n] // Numerator; Table[a[n], {n, 0, 100}]
(* or, simply: *)
a[n_] := {0, 1, 1, 1, 0, -1}[[Mod[n, 6]+1]]; Table[a[n], {n, 0, 100}]

Prog

(PARI) Vec(x*(1+x^2-x^3)/((1-x)*(1-x+x^2)*(1+x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Dec 02 2016

Crossrefs

Cf. A189733, A194767, A267068.

Sequence in context: A190201 A189702 A168395 * A130854 A165191 A189576

Adjacent sequences: A278715 A278716 A278717 * A278719 A278720 A278721

Keyword

frac,sign,easy

Author

Jean-François Alcover and Paul Curtz, Nov 30 2016

Status

approved