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%I #29 May 31 2023 13:32:58
%S 1,0,2,-2,6,-10,22,-42,86,-170,342,-682,1366,-2730,5462,-10922,21846,
%T -43690,87382,-174762,349526,-699050,1398102,-2796202,5592406,
%U -11184810,22369622,-44739242,89478486,-178956970,357913942,-715827882,1431655766,-2863311530,5726623062
%N G.f.: (1+x)/(1+x-2*x^2).
%C Or, g.f. = (1+x)/((1-x)*(1-2*x)).
%C A signed version of A078008, which is the main entry.
%C [1, 0, 2, -2, 6, -10, 22, -42, 86, ...] = an operator for toothpick sequences. The sequence convolved with A151548 = toothpick sequence A139250. The sequence convolved with A151555 = toothpick sequence A153006. - _Gary W. Adamson_, May 25 2009
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2).
%F From _R. J. Mathar_, Jul 08 2009: (Start)
%F a(n) = (2 + (-2)^n)/3 = (-1)^n*A078008(n), n>=0.
%F a(n) = 2*A077925(n-2), n>1. (End)
%F a(n) = A084247(n+1)/2. - _Philippe Deléham_, Sep 21 2009
%F G.f.: 1 + x - x*Q(0), where Q(k) = 1 + 2*x^2 - (2*k+3)*x + x*(2*k+1 - 2*x)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Oct 05 2013
%t CoefficientList[Series[(1+x)/(1+x-2x^2),{x,0,40}],x] (* or *) LinearRecurrence[{-1,2},{1,0},40] (* _Harvey P. Dale_, May 31 2023 *)
%Y Cf. A078008, A077925, A084247.
%Y Cf. A139250, A151548, A151555.
%K sign
%O 0,3
%A _N. J. A. Sloane_, May 25 2009, based on a suggestion from _Gary W. Adamson_
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