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A115055 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). +0
1
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; listen)
OFFSET

1,6

COMMENT

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.

REFERENCES

J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see Figure 2.5 p. 62

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)

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}]

CROSSREFS

Sequence in context: A147994 A106365 A086636 this_sequence A158468 A100052 A128504

Adjacent sequences: A115052 A115053 A115054 this_sequence A115056 A115057 A115058

KEYWORD

nonn,uned

AUTHOR

Roger Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2006

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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