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A123219 16 X 16 vector matrix Markov from 2nd level matrix self-similarity of the Sqrt[2] silver mean (A001333): A001333[n]^4,A090390[n]^2. +0
1
1, 1, 81, 2401, 83521, 2825761, 96059601, 3262808641, 110841719041, 3765342321601, 127910874833361, 4345203949621921, 147609026049038401, 5014361666349715681, 170340687719412376401, 5786569020271612560001 (list; graph; listen)
OFFSET

1,3

FORMULA

M2={{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 4, 2, 4, 4, 8}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2}, {0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 4}, {0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4}, {0, 0, 0, 0, 1, 2, 2, 4, 0, 0, 0, 0, 2, 4, 4, 8}, {0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4}, {0, 0, 1, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, 0, 4, 8}, {0, 1, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 8}, {1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16}} v[1] = Table[1, {n, 0, 15}] v[n_] := v[n] = M2.v[n - 1] a(n) = v[n][[1]]

MATHEMATICA

a = {{0, 1}, {1, 2}}; t[n_, m_] := a[[n, m]]; a = Table[t[n, m]*t[i, j], {n, 1, 2}, {m, 1, 2}, {i, 1, 2}, {j, 1, 2}]; M = Flatten[Table[{Flatten[Table[a[[ n, m]][[1, i]], {n, 1, 2}, {i, 1, 2}]], Flatten[Table[a[[n, m]][[2, i]], {n, 1, 2}, {i, 1, 2}]]}, {m, 1, 2}], 1]; aa = Table[M[[n, m]]*M[[i, j]], {n, 1, 4}, {m, 1, 4}, {i, 1, 4}, {j, 1, 4}]; M2 = Flatten[Table[{Flatten[Table[aa[[ n, m]][[1, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[n, m]][[2, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[ n, m]][[3, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[ n, m]][[4, i]], {n, 1, 4}, {i, 1, 4}]]}, {m, 1, 4}], 1]; v[1] = Table[1, {n, 0, 15}]; v[n_] := v[n] = M2.v[n - 1]; a = Table[v[n][[1]], {n, 1, 50}]

CROSSREFS

Cf. A001333, A090390, A120717, A121801.

Sequence in context: A016840 A128832 A085877 this_sequence A018223 A038398 A017797

Adjacent sequences: A123216 A123217 A123218 this_sequence A123220 A123221 A123222

KEYWORD

nonn,uned

AUTHOR

Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 05 2006

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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