A263013 a(0) = -a(1) = a(2) = 1, a(n) = 0 for n>2.

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

Links

Table of n, a(n) for n=0..85.

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

Cf. A000124, A010892, A130716, A161680.

Sequence in context: A188395 A266678 A267936 * A130716 A014102 A014195

Adjacent sequences: A263010 A263011 A263012 * A263014 A263015 A263016

Keyword

sign,easy

Author

Michael Somos, Oct 07 2015

Status

approved