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

Author

Paul Barry, Nov 04 2005

Keywords

• easy
• sign

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

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

Crossrefs

Cf. A113680.

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

Programs

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 *)

Formula

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