0,4

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.

Y. C. Fung, A First Course in Continuum Mechanics, Prentice Hall, New Jersey,1969, page 113

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]

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}]

Quadrisections: A001542, A001653. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2008]

Sequence in context: A072996 A153107 A020855 this_sequence A082571 A087300 A074455

Adjacent sequences: A116555 A116556 A116557 this_sequence A116559 A116560 A116561

nonn,uned,probation,obsc

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 16 2006