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A163818 Expansion of (1 - x) * (1 - x^6) / ((1 - x^2) * (1 - x^5)) in powers of x. 3
1, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
Euler transform of length 6 sequence [-1, 1, 0, 0, 1, -1].
a(5*n) = 0 unless n=0. a(5*n + 1) = a(5*n + 3) = -1, a(5*n + 2) = a(5*n + 4) = a(0) = 1.
a(n) = -a(-n) unless n=0. a(n+5) = a(n) unless n=0 or n=-5.
G.f.: (1 + x^2 + x^4) / (1 + x + x^2 + x^3 + x^4).
G.f.: 1 / (1 + x / (1 + x^4 / (1 + x^2))). - Michael Somos, Jan 03 2013
a(n) = (-1)^n * A163812(n). Convolution inverse of A163817.
EXAMPLE
G.f. = 1 - x + x^2 - x^3 + x^4 - x^6 + x^7 - x^8 + x^9 - x^11 + x^12 - x^13 + ...
MATHEMATICA
a[ n_] := Boole[n == 0] + {-1, 1, -1, 1, 0}[[Mod[n, 5, 1]]]; (* Michael Somos, Jun 17 2015 *)
a[ n_] := Boole[n == 0] + (-1)^(n + Quotient[n, 5]) Sign@Mod[n, 5]; (* Michael Somos, Jun 17 2015 *)
CoefficientList[Series[(1 + x^2 + x^4) / (1 + x + x^2 + x^3 + x^4), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 05 2017 *)
PROG
(PARI) {a(n) = (n==0) + [ 0, -1, 1, -1, 1][n%5 + 1]};
(PARI) {a(n) = (n==0) + (-1)^(n + n\5) * kronecker(25, n)};
CROSSREFS
Sequence in context: A167020 A236862 A163812 * A345009 A071040 A336834
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 04 2009
STATUS
approved

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Last modified June 22 14:17 EDT 2024. Contains 373587 sequences. (Running on oeis4.)