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A163805 Expansion of (1 - x) * (1 - x^6) / ((1 - x^3) * (1 - x^4)) in powers of x. 4
1, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
Euler transform of length 6 sequence [ -1, 0, 1, 1, 0, -1].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (2 - v) - u * (2 - u) * (3 - 2*v).
a(2*n) = 0 unless n=0, a(4*n + 1) = -1, a(4*n + 3) = a(0) = 1.
a(-n) = -a(n) unless n=0. a(n+4) = a(n) unless n=0 or n=-4.
a(n) = - A117569(n) unless n=0. a(n) = (-1)^n * A117569(n).
Convolution inverse of A163806.
G.f.: (1 - x + x^2) / (1 + x^2).
G.f. A(x) = 1 - x / (1 + x^2) = 1 / (1 + x / (1 - x / (1 + x / (1 - x)))). - Michael Somos, Jan 03 2013
a(n) = A101455(n-2) = A056594(n-3), n>2. - R. J. Mathar, Aug 06 2009
EXAMPLE
G.f. = 1 - x + x^3 - x^5 + x^7 - x^9 + x^11 - x^13 + x^15 - x^17 + x^19 + ...
MATHEMATICA
a[ n_] := Boole[n == 0] + {-1, 0, 1, 0}[[Mod[n, 4, 1]]]; (* Michael Somos, Sep 06 2015 *)
PROG
(PARI) {a(n) = (n==0) + [0, -1, 0, 1][n%4 + 1]};
(PARI) {a(n) = (n==0) - kronecker(-4, n)};
CROSSREFS
Sequence in context: A073097 A117569 A135528 * A267015 A078387 A189292
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 04 2009
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)