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}};

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

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

Table of n, a(n) for n=1..68.

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