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A263013
a(0) = -a(1) = a(2) = 1, a(n) = 0 for n>2.
0
1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0
COMMENTS
The binomial transform is 1, 0, 0, 1, 3, 6, 10, 15,..., i.e. A161680 with a 1 in front. The inverse binomial transform is 1, -2, 4, -7, 11, -16, 22, -29, 37, -46, 56,.. a variant of A000124. - R. J. Mathar, Feb 16 2023
FORMULA
Euler transform of length 6 sequence [ -1, 1, 1, 0, 0, -1].
Given g.f. A(x), then B(q) = A(q) / q satisfies 0 = f(B(q), B(q^2)) where f(u, v) = 2 + v - u * (u + 2).
G.f.: (1 + x^3) / (1 + x).
a(n) = (-1)^n * A130716(n).
G.f. is the sixth cyclotomic polynomial.
Convolution inverse is A010892.
EXAMPLE
G.f. = 1 - x + x^2.
G.f. = 1/q - 1 + q.
MATHEMATICA
PadRight[{1, -1, 1}, 100] (* Paolo Xausa, Feb 09 2024 *)
PROG
(PARI) {a(n) = (-1)^n * (n>=0 && n<=2)};
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Oct 07 2015
STATUS
approved