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A133379 Vector Markov with characteristic polynomial: 160264 + 80136 x - 49 x^2 - x^3. 0
0, 1, 1, 80087, -3683863, 6598521383, -605702530167, 557868142906439, -74816611528953111, 48274263154574414055, -8271536696003575251895, 4261821240829074290673031, -863940478961362432734725719, 382532760867137139577205872167 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..14.

Index entries for linear recurrences with constant coefficients, signature (-49,80136,160264).

FORMULA

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]].

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

EXAMPLE

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

omega=alpha-d0

50*omega=46*alpha+4*d1

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

MATHEMATICA

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}]

CROSSREFS

Sequence in context: A106775 A258951 A234756 * A250335 A250080 A251377

Adjacent sequences:  A133376 A133377 A133378 * A133380 A133381 A133382

KEYWORD

uned,sign,easy

AUTHOR

Roger L. Bagula, Oct 28 2007

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)