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%I #5 Jul 03 2023 08:01:38
%S 1,1,1,2,6,21,76,277,1011,3691,13476,49202,179641,655886,2394701,
%T 8743277,31922521,116552106,425542626,1553695877,5672688776,
%U 20711516601,75619681751,276094521627,1008046888156,3680473349246,13437751987201
%N a(n)= 4*a(n-1) -a(n-2) -a(n-3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -1, -1).
%F G.f.: (1-3*x-2*x^2)/(1-4*x+x^2+x^3). [Sep 28 2009]
%t p = Expand[(x^3 - x^2 - x - 1)*(x^3 - 4*x^2 + x + 1)] v[0] = {1, 1, 1}; M = {{0, 1, 0}, {0, 0, 1}, {-1, -1, 4}}; Det[M - x*IdentityMatrix[3]] NSolve[Det[M - x*IdentityMatrix[3]] == 0, x] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 0, 50}]
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, Jun 05 2005
%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009