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A114543
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Large integer characteristic polynomial vector Markov sequence.
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0
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0, 1, 1, 772, 2308, 597520, 2967568, 464830528, 3208753216, 363407352064, 3191137173760, 285479120733184, 3021751590913024, 225291467904913408, 2771288157631025152, 178566423666235555840, 2485482152393098412032
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The characteristic polynomal gives three real roots and an integer root of -2: x^3-772*x-1536 NSolve[Det[M - IdentityMatrix[3]*x] == 0, x] {{x -> -26.7308}, {x -> -2.}, {x -> 28.7308}} 1+/-Sqrt[769]: 769 is a prime.
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FORMULA
| M = {{0, 1, 0}, {0, 0, 1}, {1536, 772, 0}}; w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a(n) = w[n][[1]]
a(0)=0, a(1)=1, a(2)=1, a(n)=772*a(n-2)+1536*a(n-3) [From Harvey P. Dale, Nov 25 2011]
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MATHEMATICA
| M = {{0, 1, 0}, {0, 0, 1}, {1536, 772, 0}}; w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n][[1]], {n, 0, 25}]]
LinearRecurrence[{0, 772, 1536}, {0, 1, 1}, 20] (* From Harvey P. Dale, Nov 25 2011 *)
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CROSSREFS
| Sequence in context: A205622 A205357 A045078 * A133963 A133964 A033919
Adjacent sequences: A114540 A114541 A114542 * A114544 A114545 A114546
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2006
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