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A158779
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Expansion of (1+8*x+72*x^2+648*x^3)/(1-x-6561*x^4).
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0
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1, 9, 81, 729, 7290, 66339, 597780, 5380749, 53210439, 488460618, 4410495198, 39713589387, 388827279666, 3593617394364, 32530876388442, 293091736356549, 2844187518245175, 26421911242667379, 239856991227235341
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Can be generated by multiplying the sum of the top-row elements of the n-th power of the matrix [ (0,3,0,0), (0,0,3,0), (0,0,0,3), (3,0,0,1/3)] by 3^n.
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FORMULA
| a(n)= a(n-1)+6561*a(n-4). [From R. J. Mathar, Mar 31 2009]
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MATHEMATICA
| 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
| Sequence in context: A001019 A074118 A050739 * A047901 A061587 A033145
Adjacent sequences: A158776 A158777 A158778 * A158780 A158781 A158782
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 26 2009
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