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A105243
Tensor 2 X 2 X 2 matrix Fibonacci isomer in which the second matrix is altered.
0
0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 3, 0, 2, 1, 1, 0, 1, 2, 3, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 3, 5, 0, 3, 2, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 3, 5, 0, 3, 2, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 3, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 5, 8, 0, 5, 3, 3, 0, 3, 2, 4, 0, 2, 2
OFFSET
1,10
COMMENTS
Experimentation shows that these are tensors that build up in a triangular manner. This particular isomer of the M tensor give the first column of the triangular form to be a Fibonacci sequence.
FORMULA
v[1]={{0, 1}, {1, 1}} v[m]=M.v[n-1] M={M1, M2} M1={{0, 1}, {1, 0}} M2={{1, 1}, {1, 0}} a(n) = Flatten[Table[v[m], {m, 1, w}]]
MATHEMATICA
v[1] = {{0, 1}, {1, 1}} M = {{{0, 1}, {1, 0}}, {{1, 1}, {1, 0}}} v[n_] := v[n] = M.v[n - 1] a = Table[v[n], {n, 1, 6}] (*shows the triangular form*) MatrixForm[a] aa = Flatten[a] (* shows a self-similar shape to the flattened sequence*) ListPlot[aa, PlotJoined -> True]
CROSSREFS
Sequence in context: A101660 A276771 A062984 * A140081 A280596 A112345
KEYWORD
nonn,uned,obsc
AUTHOR
Roger L. Bagula, Apr 12 2005
STATUS
approved