A113975 Absolute value of the n-th coefficient in the expansion of the generating function (2-7*x-x^2) / (1-x).

2, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset

0,1

Comments

I call it the devil's Farey because of the 6,6,6 structure.

Links

Table of n, a(n) for n=0..86.

Formula

a(n) = abs([x^n] x * (1 + 2/x - 6/(1-x))).

a(n) = abs([x^n] (2-7*x-x^2) / (1-x)).

a(n) = 6 for all n >= 2.

Mathematica

a = 1; b = 2; c = 3; d = 3; e = 0; f = -1 p[x_] = FullSimplify[ExpandAll[(x - a)*(x - b)*(x - c)/((x - d)*(x - e)*(x -f))]] a = Abs[ReplacePart[Table[Abs[Coefficient[Series[p[x], {x, 0, 30}], x^n]], {n, -1, 30}], -5, 2]]

Crossrefs

Cf. A010722, A113923.

Sequence in context: A008294 A019694 A233588 * A035585 A239868 A159076

Adjacent sequences: A113972 A113973 A113974 * A113976 A113977 A113978

Keyword

nonn,dumb,less,changed

Author

Roger L. Bagula, Jan 31 2006

Extensions

Edited by Sean A. Irvine, Jul 07 2026

Status

approved