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%I #13 Sep 08 2022 08:45:27
%S 0,43,75,303,853,2786,8608,27261,85646,270137,851245,2684011,8462548,
%T 26684106,84143305,265331874,836695587,2638426981,8320048505,
%U 26236520890,82734709152,260896992401,822717574538,2594372978149
%N Expansion of x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5).
%H G. C. Greubel, <a href="/A121957/b121957.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,-7,-12,2).
%F From _R. J. Mathar_, Apr 04 2009: (Start)
%F a(n) = 2*a(n-1) + 7*a(n-2) - 7*a(n-3) - 12*a(n-4) + 2*a(n-5).
%F G.f.: x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5). (End)
%t M = {{0,1,0,0,1,1,0,0,0,1}, {1,0,1,0,0,1,1,0,0,0}, {0,1,0,1,0,0,1,1,0,0}, {0,0,1, 0,1,0,0,0,1,0}, {1,0,0,1,0,0,0,0,1,1}, {1,1,0,0,0,0,0,0,0,0}, {0,1,1,0,0,0,0,0,0, 0}, {0,0,1,1,0,0,0,0,0,0}, {0,0,0,1,1,0,0,0,0,0}, {1,0,0,0,1,0,0,0,0,0}};
%t v[1]= Table[Fibonacci[n], {n,0,9}]; v[n_]:= v[n]= M.v[n-1];
%t Table[Floor[v[n][[1]]], {n, 1, 50}]
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5) )); // _G. C. Greubel_, Jul 12 2021
%o (Sage)
%o def A121957_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x^2*(43-11*x-148*x^2+23*x^3)/(1-2*x-7*x^2+7*x^3+12*x^4 -2*x^5) ).list()
%o a=A121957_list(50); a[1:] # _G. C. Greubel_, Jul 12 2021
%K nonn,easy
%O 1,2
%A _Roger L. Bagula_, Sep 01 2006
%E Edited by _G. C. Greubel_, Jul 12 2021
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