A107476 - OEIS

%I #7 Jun 13 2015 00:51:49

%S 0,1,1,2,3,5,4,-13,-157,-1050,-6575,-39949,-241792,-1459663,-8809863,

%T -53159766,-320770109,-1935508203,-11678751308,-70468796429,

%U -425204036789

%N Expansion of -x*(-1+5*x+8*x^2-11*x^3+3*x^4)/(1-6*x-4*x^2+24*x^3-6*x^4-4*x^5+x^6) .

%C The sequence is generated by taking increasing powers of the matrix M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, 4, 6, -24, 4, 6}}, multiplying the vector {0, 1, 1, 2, 3, 5} from the right and storing the product's upper element.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (6,4,-24,6,4,-1).

%t m=4 M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, m, (m + 2), -m*(m + 2), m, (m + 2)}} v[0] = {0, 1, 1, 2, 3, 5} v[n_] := M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]

%K sign

%O 0,4

%A _Roger L. Bagula_, May 27 2005

%E Signed version reintroduced. - R. J. Mathar, Sep 11 2011