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Expansion of -x*(47*x^3+25*x^2+5*x+1)/(38*x^4+54*x^3+22*x^2-1).
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%I #19 Oct 27 2015 15:58:55

%S 1,5,47,211,1342,7370,42704,242626,1388464,7923848,45270764,258521500,

%T 1476606232,8433200480,48165787136,275090964088,1571151179728,

%U 8973415333520,51250537925936,292710757678096,1671780007210336

%N Expansion of -x*(47*x^3+25*x^2+5*x+1)/(38*x^4+54*x^3+22*x^2-1).

%D R. G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, New York, 1966, pp. 557ff.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,22,54,38).

%F G.f.: -x*(47*x^3+25*x^2+5*x+1)/(38*x^4+54*x^3+22*x^2-1). - _Colin Barker_, Nov 02 2012

%t M = {{0, 1, 1, 2}, {2, 0, 2, 1}, {3, 3, 0, 1}, {3, 3, 2, 0}}; v[1] = {1, 2, 3, 0}; v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[1]], {n, 1, 50}]

%t LinearRecurrence[{0,22,54,38},{1,5,47,211},30] (* _Harvey P. Dale_, Oct 27 2015 *)

%K nonn,less,easy

%O 1,2

%A _Roger L. Bagula_, Sep 15 2006

%E New name (using g.f. by _Colin Barker_), _Joerg Arndt_, Mar 30 2014