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 A098023 M={{0, 1, -1, 1}, {-1, 0, 1, -1}, {1, -1, 0, 1}, {-1, 1, -1, 0}}; a[n_]:=M.a[n-1]-Sum [a[n-1][[i, i]], {i, 1, 4}]*M/n; a[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}}; 1
 34, 31, 9, 8, 25, 39, 22, 5, 3, 22, 41, 17, 20, 7, 35, 18, 8, 54, 98, 40, 51, 16, 85, 43, 79, 77, 22, 21, 62, 92, 54, 14, 60, 97, 53, 38, 61, 91, 42, 33, 19, 42, 105, 9, 34, 39, 117, 28, 46, 94, 264, 14, 75, 94, 275, 57, 155, 227, 128, 99, 140, 230, 94, 80, 233, 459, 309, 327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These types of matrices are used in Kernel inversion functions in scattering theory. REFERENCES Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254. LINKS MATHEMATICA (* SO(4) Determinant one 4 X 4 Markov Fredholm-like sequence *) (* page 254 Scattering Theory of Waves and Particles by Roger G. Newton 1966 McGraw Hill*) (* by Roger L. Bagula, Sep 09 2004 *) Clear[M, A, x] digits=8; M={{0, 1, -1, 1}, {-1, 0, 1, -1}, {1, -1, 0, 1}, {-1, 1, -1, 0}}; Det[M] A[n_]:=M.A[n-1]-Sum[A[n-1][[i, i]], {i, 1, 4}]*M/n; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}}; (* flattened sequence of 4 X 4 matrices made with an SO(4) Determinant one Fredholm-like recurrence*) b=Flatten[Table[M.A[n], {n, 1, digits}]] Floor[Abs[b]] Dimensions[b][[1]] ListPlot[b, PlotJoined->True] CROSSREFS Sequence in context: A070727 A298894 A204632 * A302209 A022990 A023476 Adjacent sequences:  A098020 A098021 A098022 * A098024 A098025 A098026 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Sep 09 2004 STATUS approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)