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%I #8 Jun 13 2015 00:52:08
%S 0,159,4846,43648,272432,1759444,10596296,64633588,387979832,
%T 2337067204,14023337096,84221417428,505334268632,3032732926564,
%U 18196438915496,109185158327668,655111280131832,3930726320267524,23584360724983496
%N 1045*6^n/27-513*2^(n-2)-2072*3^(n-3)+670*(-1)^n*3^(n-3)+254*(-1)^(n+1), n>1.
%C Unique structure in that all the secular roots are Integers.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,5,-75,36,108).
%F a(n)= 7*a(n-1) +5*a(n-2) -75*a(n-3) +36*a(n-4) +108*a(n-5), n>6. [Oct 14 2009]
%F G.f.: x^2*(-159-3733*x-8931*x^2+45409*x^3+8094*x^4)/( (6*x-1)*(3*x-1) * (2*x-1) * (3*x+1) * (1+x)). [Oct 14 2009]
%t M = {{0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0}}; v[1] = Table[Fibonacci[n], {n, 0, 17}] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
%t LinearRecurrence[{7,5,-75,36,108},{0,159,4846,43648,272432,1759444},20] (* _Harvey P. Dale_, May 20 2015 *)
%K nonn
%O 1,2
%A _Roger L. Bagula_, Aug 28 2006
%E Definition replaced by formula - The Assoc. Editors of the OEIS, Oct 14 2009