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%I #7 Oct 02 2021 17:37:05
%S 0,1,1,2,7,41,272,1853,12677,86794,594315,4069613,27867056,190822393,
%T 1306675145,8947587010,61269485263,419548848433,2872902154816,
%U 19672481099861,134709256274733,922434929990986,6316464240083059
%N a(n) = 7*a(n-1)-7*a(n-3)-a(n-4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,0,-7,-1).
%F G.f.: x*(1-6*x-5*x^2)/(1-7*x+7*x^3+x^4). [Sep 28 2009]
%t m = 7 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-1, -m, 0, m}} Expand[Det[M - x*IdentityMatrix[4]]] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits = 50; a = Table[v[n][[1]], {n, 1, digits}]
%t LinearRecurrence[{7,0,-7,-1},{0,1,1,2},30] (* _Harvey P. Dale_, Oct 02 2021 *)
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, May 24 2005
%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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