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%I #11 Sep 18 2017 10:27:59
%S 1,1,1,1,1,0,-1,-6,-12,-32,-59,-134,-244,-519,-948,-1949,-3586,-7225,
%T -13397,-26640,-49744,-98024,-184114,-360455,-680247,-1325397,
%U -2510702,-4874298,-9260629,-17929771,-34142684,-65967689,-125841523,-242755543,-463720287,-893457507,-1708515146
%N a(1) = 1; a(2) = 1; a(3) = 1; a(4) = 1; a(5) = 1; a(n) = a(n-1)+4a(n-2)-3a(n-3)-3a(n-4)+a(n-5) for n >= 6.
%H Peter Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
%F G.f.: -(2*x-1)*(x+1)*(x^2-x-1)/(-1+x^5-3*x^4-3*x^3+4*x^2+x). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%p a[1]:=1: a[2]:=1: a[3]:=1: a[4]:=1: a[5]:=1: for n from 6 to 37 do a[n]:=a[n-1]+4*a[n-2]-3*a[n-3]-3*a[n-4]+a[n-5] od: seq(a[n],n=1..37);
%t M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, -3, -3, 4, 1}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
%Y Cf. A066170.
%K sign
%O 1,8
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 20 2006
%E Edited by _N. J. A. Sloane_, Oct 08 2006
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