A098023 - OEIS

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

(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

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