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A116558
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Alternating four direction limiting simple shear Markov sequence.
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0
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0, 1, 1, 5, 2, 5, 5, 29, 12, 29, 29, 169, 70, 169, 169, 985, 408, 985, 985, 5741, 2378, 5741, 5741, 33461, 13860, 33461, 13860, 33461, 33461, 195025, 80782, 195025, 195025, 1136689, 470832, 1136689, 1136689, 6625109, 2744210, 6625109, 6625109, 38613965, 15994428, 38613965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| All the stress tensors has determinant two and act serially from four different directions. The second part also has a chaotic output: b = Table[v[n][[2]], {n, 0, 25}] {1, 0, 2, 2, 9, 2, 12, 12, 53, 12, 70, 70, 309, 70, 408, 408, 1801, 408, 2378, 2378, 10497, 2378, 13860, 13860, 61181, 13860} In metals this causes rapid metal fatigue, heating and material failure.
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REFERENCES
| Y. C. Fung, A First Course in Continuum Mechanics, Prentice Hall, New Jersey,1969, page 113
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FORMULA
| M1 = {{0, -1}, {1, 2}}; M2 = {{2, 1}, {-1, 0}}; M3 = {{1, 2}, {0, 1}}; M4 = {{1, 0}, {2, 1}}; M[n_] = If[Mod[n, 4] == 0, M1, If[Mod[n, 4] == 1, M2, If[ Mod[n, 4] == 3, M3, M4]]]; v[0] = {0, 1}; v[n_] := v[n] = M[n].v[n - 1] a(n) = v[n][[1]]
a(n)=6*a(n-4)-a(n-8). G.f.: x(1+x+5x^2+2x^3-x^4-x^5-x^6) / ((1-2x^2-x^4) (1+2x^2-x^4)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2008]
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MATHEMATICA
| M1 = {{0, -1}, {1, 2}}; M2 = {{2, 1}, {-1, 0}}; M3 = {{1, 2}, {0, 1}}; M4 = {{1, 0}, {2, 1}}; M[n_] = If[Mod[n, 4] == 0, M1, If[Mod[n, 4] == 1, M2, If[ Mod[n, 4] == 3, M3, M4]]]; v[0] = {0, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[Abs[v[n][[1]]], {n, 0, 25}]
CoefficientList[Series[x (1+x+5x^2+2x^3-x^4-x^5-x^6)/((1-2x^2-x^4) (1+2x^2-x^4)), {x, 0, 50}], x] (* From Harvey P. Dale, May 11 2011 *)
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CROSSREFS
| Quadrisections: A001542, A001653. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2008]
Sequence in context: A199957 A020855 A191583 * A196626 A082571 A087300
Adjacent sequences: A116555 A116556 A116557 * A116559 A116560 A116561
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KEYWORD
| nonn,uned,obsc
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 16 2006
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