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Search: id:A158779
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| A158779 |
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A vector matrix Markov sequence :t=3; M={{0, t, 0, 0}, {0, 0, t, 0}, {0, 0, 0, t}, {t, 0, 0, 1/t}}. |
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1
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| 1, 9, 81, 729, 7290, 66339, 597780, 5380749, 53210439, 488460618, 4410495198, 39713589387, 388827279666, 3593617394364, 32530876388442, 293091736356549, 2844187518245175, 26421911242667379, 239856991227235341
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OFFSET
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0,2
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COMMENT
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Characteristic polynomial is: t=3;
-t^4 - x^3/t + x^4
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FORMULA
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t=3;
M={{0, t, 0, 0},
{0, 0, t, 0},
{0, 0, 0, t},
{t, 0, 0, 1/t}}.
v(n)=M.v(n-1);
a(n)=v(n)[[1]].
Apparently a(n)= a(n-1)+6561*a(n-4) and therefore g.f. = -(1+8*x+72*x^2+648*x^3)/(-1+x+6561*x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2009]
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MATHEMATICA
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Clear[M, v, t, n];
M = {{0, t, 0, 0}, {0, 0, t, 0}, {0, 0, 0, t}, {t, 0, 0, 1/t}};
v[0] = {1, 1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 3;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A001019 A074118 A050739 this_sequence A047901 A061587 A033145
Adjacent sequences: A158776 A158777 A158778 this_sequence A158780 A158781 A158782
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 26 2009
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