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Search: id:A120718
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| A120718 |
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First level Hadamard-Sylvester matrix self-similarity for the 2 X 2 Fibonacci matrix as a 4 X 4 matrix Markov ( made using an array repartitioning method) Characteristic Ploynomial:1 - x - 4 x^2 - x^3 + x^4. |
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| 0, 3, 6, 18, 45, 120, 312, 819, 2142, 5610, 14685, 38448, 100656, 263523, 689910, 1806210, 4728717, 12379944, 32411112, 84853395, 222149070, 581593818, 1522632381, 3986303328, 10436277600, 27322529475, 71531310822, 187271402994
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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t[n_, m_] := If[ n == m == 1, 0, 1] 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] v[1] = {0, 1, 2, 3} v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]
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MATHEMATICA
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t[n_, m_] := If[ n == m == 1, 0, 1] 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] v[1] = {0, 1, 2, 3} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}] Det[M - x*IdentityMatrix[4]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[4]] == 0, x][[n]], {n, 1, 4}] Abs[aaa] a1 = Table[N[a[[n]]/a[[n - 1]]], {n, 7, 50}]
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CROSSREFS
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Cf. A000045, A072845.
Sequence in context: A081150 A007990 A121188 this_sequence A032120 A115344 A108507
Adjacent sequences: A120715 A120716 A120717 this_sequence A120719 A120720 A120721
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Aug 13 2006
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