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A133379
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Vector Markov with characteristic polynomial: 160264 + 80136 x - 49 x^2 - x^3.
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0
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0, 1, 1, 80087, -3683863, 6598521383, -605702530167, 557868142906439, -74816611528953111, 48274263154574414055, -8271536696003575251895, 4261821240829074290673031, -863940478961362432734725719, 382532760867137139577205872167
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OFFSET
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1,4
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COMMENTS
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Limiting ratio is root:-307.723 Polynomial roots are all real numbers: {-307.723, -1.99756, 260.721}
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LINKS
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Table of n, a(n) for n=1..14.
Index entries for linear recurrences with constant coefficients, signature (-49,80136,160264).
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FORMULA
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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]
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EXAMPLE
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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
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A106775 A258951 A234756 * A250335 A250080 A251377
Adjacent sequences: A133376 A133377 A133378 * A133380 A133381 A133382
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KEYWORD
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uned,sign,easy
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AUTHOR
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Roger L. Bagula, Oct 28 2007
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STATUS
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approved
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