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Search: id:A122996
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| A122996 |
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A rational vector matrix Markov with 1/7 coefficient: characteristic Polynomial: -1 - x/7 + x^2. |
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+0
1
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| 1, 7, 56, 399, 3143, 22694, 176701, 1288707, 9947056, 73093699, 560499443, 4142090694, 31606563401, 234569007407, 1783290614056, 13277171976999, 100658412065743, 751239838938694, 5683502030160101, 42494254138156107
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Two real roots: NSolve[Det[M - x*IdentityMatrix[2]] == 0, x] {{x -> -0.931119}, {x -> 1.07398}} Relative ratio is very small: limit[(a[[n + 1]]/a[[n]])/7,n->Infinity]=1.07398
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FORMULA
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M := {{0, 1}, {1, 1/7}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) =v[n][[1]]*7^(n - 1)
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MATHEMATICA
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M := {{0, 1}, {1, 1/7}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]]*7^(n - 1), {n, 1, 30}]
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CROSSREFS
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Cf. A026597.
Sequence in context: A082140 A054614 A104896 this_sequence A092315 A092318 A057090
Adjacent sequences: A122993 A122994 A122995 this_sequence A122997 A122998 A122999
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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), Sep 22 2006
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