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%I #17 Sep 19 2017 04:28:43
%S 1,-2,1,-4,0,-9,-5,-23,-24,-65,-90,-196,-311,-613,-1039,-1954,-3419,
%T -6288,-11172,-20329,-36385,-65871,-118312,-213669,-384422,-693448,
%U -1248623,-2251097,-4054895,-7308466,-13167159,-23729196,-42755048,-77046281,-138827181,-250164695,-450772776
%N Expansion of x*(1 - 3*x + x^2) / (1 - x - 2*x^2 + x^3).
%H P. Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. 70 (1997), no. 1, 22-31.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1).
%F a(n) = A006053(n+1) - 3*A006053(n) + A006053(n-1). - _R. J. Mathar_, Nov 07 2011
%t M = {{0, -1, -1}, {-1, 0, 0}, {-1, 0, 1}}; v[1] = {1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
%o (PARI) Vec( x*(1 - 3*x + x^2) / (1 - x - 2*x^2 + x^3) + O(x^50)) \\ _Michel Marcus_, Sep 19 2017
%K easy,sign
%O 1,2
%A _Gary W. Adamson_ and _Roger L. Bagula_, Oct 17 2006