A113679 Expansion of (1-x-2x^2)/(1-x).

1, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2

Offset

0,3

Comments

From Gary W. Adamson, Mar 06 2012: (Start)

Signed (1, 0, -2, 2, -2, 2, ...) and convolved with the Toothpick sequence A139250 = A151548: (1, 3, 5, 7, 5, 11, ...). The inverse of (1, 0, -2, 2, -2, ...) = A151575: (1, 0, 2, -2, 6, -10, 22, ...).

The unsigned sequence convolved with:

(1, 2, 3, ...) = A002523, (n^2 + 1). Convolved with:

(A001045) = .... A097064: (1, 1, 5, 9, 21, 41, ...).

(End)

Links

Table of n, a(n) for n=0..66.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = C(0, n) + 2*C(1, n) - 2.

Mathematica

CoefficientList[Series[(1-x-2x^2)/(1-x), {x, 0, 80}], x] (* or *) Join[{1, 0}, PadRight[{}, 80, -2]] (* Harvey P. Dale, Mar 05 2012 *)

Crossrefs

Cf. A113680.

Cf. A139250, A151548, A151575, A002523. - Gary W. Adamson, Mar 06 2012

Sequence in context: A044930 A032545 A231560 * A262438 A044931 A178487

Adjacent sequences: A113676 A113677 A113678 * A113680 A113681 A113682

Keyword

easy,sign

Author

Paul Barry, Nov 04 2005

Status

approved