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 A133379 Vector Markov with characteristic polynomial: 160264 + 80136 x - 49 x^2 - x^3. 0

%I

%S 0,1,1,80087,-3683863,6598521383,-605702530167,557868142906439,

%T -74816611528953111,48274263154574414055,-8271536696003575251895,

%U 4261821240829074290673031,-863940478961362432734725719,382532760867137139577205872167

%N Vector Markov with characteristic polynomial: 160264 + 80136 x - 49 x^2 - x^3.

%C Limiting ratio is root:-307.723 Polynomial roots are all real numbers: {-307.723, -1.99756, 260.721}

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-49,80136,160264).

%F M = {{1, -1, 1}, {50, -46, -4}, {binomial[50, 3], -binomial[46, 3], -binomial[4, 3]}} v(n)=M*v(n-1) a(n) =v(n)[[1]].

%F G.f.: -x^2*(50*x+1)/(160264*x^3+80136*x^2-49*x-1). [_Colin Barker_, Oct 11 2012]

%e Sequence of equations in omega, alpha and {d0,d1,d2}:

%e omega=alpha-d0

%e 50*omega=46*alpha+4*d1

%e Binomial[50,3]*omega=binomial[46,3]*alpha+binomial[4,3]*d2

%t M = {{1, -1, 1}, {50, -46, -4}, {Binomial[50, 3], -Binomial[46, 3], -Binomial[4, 3]}} v[0] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]], {n, 0, 20}]

%K uned,sign,easy

%O 1,4

%A _Roger L. Bagula_, Oct 28 2007

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Last modified July 31 10:51 EDT 2021. Contains 346373 sequences. (Running on oeis4.)