This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A151575 #31 Feb 22 2025 22:33:05
%S A151575 1,0,2,-2,6,-10,22,-42,86,-170,342,-682,1366,-2730,5462,-10922,21846,
%T A151575 -43690,87382,-174762,349526,-699050,1398102,-2796202,5592406,
%U A151575 -11184810,22369622,-44739242,89478486,-178956970,357913942,-715827882,1431655766,-2863311530,5726623062
%N A151575 G.f.: (1+x)/(1+x-2*x^2).
%C A151575 Or, g.f. = (1+x)/((1-x)*(1-2*x)).
%C A151575 A signed version of A078008, which is the main entry.
%C A151575 [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 A151575 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2).
%F A151575 From _R. J. Mathar_, Jul 08 2009: (Start)
%F A151575 a(n) = (2 + (-2)^n)/3 = (-1)^n*A078008(n), n>=0.
%F A151575 a(n) = 2*A077925(n-2), n>1. (End)
%F A151575 a(n) = A084247(n+1)/2. - _Philippe Deléham_, Sep 21 2009
%F A151575 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 A151575 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 A151575 Cf. A078008, A077925, A084247.
%Y A151575 Cf. A139250, A151548, A151555.
%K A151575 sign,easy
%O A151575 0,3
%A A151575 _N. J. A. Sloane_, May 25 2009, based on a suggestion from _Gary W. Adamson_