A210357 Location of the maximum modulus in the inverse of Hilbert's matrix.

1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 46, 47, 48, 48

Offset

1,2

Comments

The maximum value always occurs on the diagonal. These numbers are close to n/sqrt(2).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Mathematica

Table[im = Inverse[HilbertMatrix[n]]; pos = Position[im, Max[Abs[Flatten[im]]]]; If[Length[pos] > 1, Print[{n, pos}]; 0, pos[[1, 1]]], {n, 70}]
Table[t = Table[(2*i-1) Binomial[n+i-1, n-i]^2 * Binomial[2*i-2, i-1]^2, {i, n}]; Position[t, Max[t]][[1, 1]], {n, 100}]

Crossrefs

Cf. A210356 (largest element in the inverse of Hilbert's matrix).

Sequence in context: A064726 A274616 A257175 * A057359 A076538 A138466

Adjacent sequences: A210354 A210355 A210356 * A210358 A210359 A210360

Keyword

nonn

Author

T. D. Noe, Mar 28 2012

Status

approved