A105243 Tensor 2 X 2 X 2 matrix Fibonacci isomer in which the second matrix is altered.

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.

Links

Table of n, a(n) for n=1..105.

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

Adjacent sequences: A105240 A105241 A105242 * A105244 A105245 A105246

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Apr 12 2005

Status

approved