%I #18 Mar 12 2014 16:37:14
%S 0,1,-1,1,-1,1,-2,1,-3,2,-3,3,-5,5,-6,7,-9,10,-12,14,-17,20,-25,28,
%T -35,40,-49,57,-69,81,-98,116,-139,164,-196,233,-278,330,-395,469,
%U -559,665,-793,943,-1125,1338,-1595,1898,-2261,2692,-3206
%N a(n) = floor(d(n)/18^(n-1)) where d(n) = 0, 1, -8, 352, -5120,.. and d(n) = -8*d(n-1) +288*d(n-2).
%C The low limiting ratio is: -1.190866431897927
%F (Binet variant of the definition):
%F c = 4/(1 + sqrt(19)); b = 4/(1 - sqrt(19)); a(n) = floor[(c^n - b^n)/(c - b)].
%p A174427aux := proc(n) option remember; if n <= 1 then n ; else -8*procname(n-1)+288*procname(n-2) ; end if; end proc:
%p A174427 := proc(n) floor(A174427aux(n)/18^(n-1)) ; end proc:
%p seq(A174427(n),n=0..20) ;
%t a = 4/(1 + Sqrt[19]); b = 4/(1 - Sqrt[19]);
%t f[n_] = (a^n - b^n)/(a - b)
%t Table[Floor[f[n]], {n, 0, 50}]
%t Module[{c=Sqrt[19],a,b},a=4/(1+c);b=4/(1-c);Floor[(a^#-b^#)/(a-b)]&/@ Range[0,50]] (* _Harvey P. Dale_, Sep 16 2012 *)
%K sign
%O 0,7
%A _Roger L. Bagula_, Nov 28 2010