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Expansion of (1-x)/(1-x+2*x^2).
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%I #19 Feb 06 2022 12:57:23

%S 1,0,-2,-2,2,6,2,-10,-14,6,34,22,-46,-90,2,182,178,-186,-542,-170,914,

%T 1254,-574,-3082,-1934,4230,8098,-362,-16558,-15834,17282,48950,14386,

%U -83514,-112286,54742,279314,169830,-388798,-728458,49138,1506054,1407778,-1604330,-4419886,-1211226,7628546

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

%C Equals the INVERT transform of [1, -1, -1, 1, 1, -1, -1, 1, 1, ...], i.e., 1 followed by repeats of (-1, -1, 1, 1, ...). - _Gary W. Adamson_, Sep 16 2008

%C Pisano period lengths: 1, 1, 8, 1, 24, 8, 21, 2, 24, 24, 10, 8, 168, 21, 24, 2, 144, 24, 360, 24, ... - _R. J. Mathar_, Aug 10 2012

%H G. C. Greubel, <a href="/A078020/b078020.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2).

%F a(n) = A107920(n+1) - A107920(n). - _R. J. Mathar_, Mar 14 2011

%F a(n) = (-1)^n*(A001607(n) + A001607(n-1)). - _G. C. Greubel_, Jun 29 2019

%t LinearRecurrence[{1,-2}, {1,0}, 50] (* or *) CoefficientList[Series[(1 - x)/(1-x+2*x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 29 2019 *)

%o (PARI) Vec((1-x)/(1-x+2*x^2)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 25 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^2) )); // _G. C. Greubel_, Jun 29 2019

%o (Sage) ((1-x)/(1-x+2*x^2)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 29 2019

%o (GAP) a:=[1,0];; for n in [2..50] do a[n]:=a[n-1]-2*a[n-2]; od; a; # _G. C. Greubel_, Jun 29 2019

%Y Cf. A001607, A107920.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 17 2002