A122519 - OEIS

%I #17 Jun 13 2015 00:52:09

%S 1,1,1,1,1,3,3,3,5,7,9,11,15,21,27,35,47,63,83,109,145,193,255,337,

%T 447,593,785,1039,1377,1825,2417,3201,4241,5619,7443,9859,13061,17303,

%U 22921,30363,40223,53285,70587,93507,123871,164095,217379,287965,381473,505345,669439

%N Expansion of x * (x+1) * (x^3-x^2-1) / ((x^2+1) * (x^3+x^2-1)).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1).

%F G.f.: x*(x+1)*(x^3-x^2-1)/((x^2+1)*(x^3+x^2-1)). [_Colin Barker_, Oct 19 2012]

%t M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 0, 0}}; w[1] = {1, 1, 1, 1, 1}; w[n_] := w[n] = M.w[n - 1] a = Table[w[n][[1]], {n, 1, 30}]

%t LinearRecurrence[{0,0,1,1,1},{1,1,1,1,1},60] (* _Harvey P. Dale_, Feb 02 2015 *)

%o (PARI) Vec(x*(x+1)*(x^3-x^2-1)/((x^2+1)*(x^3+x^2-1)) + O(x^70)) \\ _Michel Marcus_, Feb 12 2015

%K nonn,easy

%O 1,6

%A _Roger L. Bagula_, Sep 16 2006

%E Sequence edited by _Joerg Arndt_, _Colin Barker_, _Bruno Berselli_, Oct 19 2012