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%I #20 Sep 08 2022 08:45:12
%S 1,-5,-17,1,121,235,-377,-2399,-2159,12475,40063,-7199,-294839,
%T -539285,985303,5745601,4594081,-31031045,-94220657,28776001,
%U 717096601,1232761195,-2554153817,-13737635999,-9596195279,76971061435,221115489823,-96566450399,-1740941329559
%N (1,1) entry of powers of the orthogonal design shown below.
%C 1 0 1 1 1 1 1 1
%C 0 1 1 -1 1 -1 -1 1
%C -1 -1 1 0 1 1 -1 -1
%C -1 1 0 1 1 -1 1 -1
%C -1 -1 -1 -1 1 0 1 1
%C -1 1 -1 1 0 1 -1 1
%C -1 1 1 -1 -1 1 1 0
%C -1 -1 1 1 -1 -1 0 1
%H G. C. Greubel, <a href="/A090592/b090592.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-7).
%F a(1) = 1, a(2) = -5, a(n) = 2*a(n-1) - 7*a(n-2). - _Philippe Deléham_, Mar 05 2012
%F G.f.: x*(1-7*x)/(1-2*x+7*x^2). - _Philippe Deléham_, Mar 05 2012
%F G.f.: G(0)/(2*x) -1/x, where G(k)= 1 + 1/(1 - x*(6*k+1)/(x*(6*k+7) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 03 2013
%t Rest[CoefficientList[Series[x*(1-7*x)/(1-2*x+7*x^2), {x, 0, 30}], x]] (* _G. C. Greubel_, Oct 22 2018 *)
%o (PARI) x='x+O('x^30); Vec(x*(1-7*x)/(1-2*x+7*x^2)) \\ _G. C. Greubel_, Oct 22 2018
%o (Magma) I:=[1,-5]; [n le 2 select I[n] else 2*Self(n-1) - 7*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Oct 22 2018
%o (GAP) a:=[1,-5];; for n in [3..30] do a[n]:=2*a[n-1]-7*a[n-2]; od; a; # _Muniru A Asiru_, Oct 23 2018
%Y Cf. A089181.
%K sign,easy
%O 1,2
%A _Simone Severini_, Dec 08 2003
%E Corrected and extended by _Philippe Deléham_, Mar 05 2012
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