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A115055
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Lower level digraph derived from a voltage graph (Gross's covering graph construction) that is generalized Fibonacci Markov in matrix terms to give a 6 X 6 Markov: Characteristic Polynomial: (-1 - x + x^2)(1 + 2 x + 2 x^2 + x^3 + x^4).
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0
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0, 1, 0, 0, 1, 3, 3, 2, 6, 15, 21, 24, 42, 86, 138, 192, 305, 546, 906, 1381, 2175, 3651, 6042, 9582, 15225, 24901, 40836, 65748, 105364, 170796, 278184, 450017, 724968, 1172412, 1902321, 3080367, 4975551, 8044478, 13029534, 21096027, 34114553
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Ratio=limit[a(n+1)/a(n),n->Infinity]=Golden Mean This digraph constuction gives a complex substructure to the Fibonacci Pisot that is not Pisot. Gross's covering graph constructions called voltage graphs are abstractions from lower level graphs.
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REFERENCES
| J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see Figure 2.5 p. 62
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FORMULA
| M = {{0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 1, 0}} v(n)=M.v(n-1) a(n)=v(n)(1)
G.f.: x/(1-(x+x^2)^3). a(n)=sum(k=0..n, binomial(3*k,n-3*k)). [From Vladimir Kruchinin, Oct 12 2011]
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MATHEMATICA
| (*Gross page 62 voltage group L3 : weights set to one*) M = {{0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 1, 0}} v[1] = {0, 0, 0, 0, 0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A106365 A200174 A086636 * A158468 A200770 A100052
Adjacent sequences: A115052 A115053 A115054 * A115056 A115057 A115058
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2006
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