%I #22 Oct 02 2023 10:36:59

%S 1,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,

%T -2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,

%U -2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2

%N Expansion of (1-x-2x^2)/(1-x).

%C From _Gary W. Adamson_, Mar 06 2012: (Start)

%C 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, ...).

%C The unsigned sequence convolved with:

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

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

%C (End)

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

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

%t 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 *)

%Y Cf. A113680.

%Y Cf. A139250, A151548, A151575, A002523. - _Gary W. Adamson_, Mar 06 2012

%K easy,sign

%O 0,3

%A _Paul Barry_, Nov 04 2005