A105240 Tensor Markov 2 X 2 X 2 times matrix 2 X 2 in a generalized Fibonacci type form: symmetrical form.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 4, 1, 1, 1, 2, 2, 2, 2, 4, 1, 1, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 1, 1, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 1, 1, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 4, 8, 8, 8, 8, 16, 1, 1, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4

Offset

1,8

Comments

The symmetry of the two component matrices in the tensor gives powers of two in the result.

Links

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

Formula

v[m]=M.v[m-1] M={M1, M2} v[1]=M1=M2={{0, 1}, {1, 1}}: Fibonacci matrix a(n) = Flatten[v[m]

Mathematica

v[1] = {{0, 1}, {1, 1}} M = {{{0, 1}, {11}}, {{0, 1}, {1, 1}}} v[n_] := v[n] = M.v[n - 1] a = Table[v[n], {n, 1, 6}] aa = Flatten[a] Length[aa]

Crossrefs

Sequence in context: A351742 A090677 A161097 * A327499 A353693 A327857

Adjacent sequences: A105237 A105238 A105239 * A105241 A105242 A105243

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Apr 12 2005

Status

approved