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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

%I

%S 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,

%T 77,22,21,62,92,54,14,60,97,53,38,61,91,42,33,19,42,105,9,34,39,117,

%U 28,46,94,264,14,75,94,275,57,155,227,128,99,140,230,94,80,233,459,309,327

%N 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}};

%C These types of matrices are used in Kernel inversion functions in scattering theory.

%D Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.

%t (* 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]

%K nonn,uned

%O 1,1

%A _Roger L. Bagula_, Sep 09 2004

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Last modified June 27 04:16 EDT 2022. Contains 354888 sequences. (Running on oeis4.)