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Search: id:A106438
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| A106438 |
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4 X 4 quartic vector Markov related by characteristic polynomial (x^4-6*x^2+9*x-1) to A001906 and A006190. |
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+0
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| 0, 2, 7, 22, 69, 218, 694, 2224, 7167, 23204, 75415, 245878, 803700, 2632502, 8637127, 28376122, 93326289, 307205138, 1011931354, 3335118004, 10996652127, 36271055864, 119668397395, 394905999598, 1303417073160, 4302619498442
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Real Roots:{{x -> -0.302776}, {x -> 0.381966}, {x -> 2.61803}, {x -> 3.30278}}
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FORMULA
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M={{0, 0, 0, 1}, {1, 3, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 3}} v[n]=M.v[n-1] a(n)=v[n][[1]]
(1/2) [Lucas(2n-1) + A006190(n+1) ]. - Ralf Stephan, Jun 2 2007
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MATHEMATICA
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v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits = 50; a = Table[v[n][[1]], {n, 1, digits}]
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CROSSREFS
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Cf. A001906, A006190.
Adjacent sequences: A106435 A106436 A106437 this_sequence A106439 A106440 A106441
Sequence in context: A037552 A094618 A077833 this_sequence A109999 A092690 A030186
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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), May 29 2005
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