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Search: id:A114543
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| A114543 |
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Large integer characteristic polynomial vector Markov sequence. |
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+0
1
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| 0, 1, 1, 772, 2308, 597520, 2967568, 464830528, 3208753216, 363407352064, 3191137173760, 285479120733184, 3021751590913024, 225291467904913408, 2771288157631025152, 178566423666235555840, 2485482152393098412032
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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
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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]]
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MATHEMATICA
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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}]]
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CROSSREFS
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Adjacent sequences: A114540 A114541 A114542 this_sequence A114544 A114545 A114546
Sequence in context: A046505 A013542 A045078 this_sequence A133963 A133964 A033919
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2006
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