A130306 Degree of the scheme of n X n complex matrices that square to zero.

1, 2, 2, 12, 28, 440, 2456, 98448, 1327632, 134302752, 4398726432, 1116577758912, 89104889764288, 56558827752672128, 11021135122877392256, 17451895365397015875840, 8316834448188073547563264, 32799202036840274283669160448, 38271513084756431661704424923648

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

A. Knutson and P. Zinn-Justin, A scheme related to the Brauer loop model, Adv. in Math. 214 (2007), 40-77.

Formula

a(2n) = 2^n * det(binomial(2i+2j+1,2i)), 0<=i,j<=n-1; a(2n+1) = 2^(n+1) * det(binomial(2i+2j+3,2i+1)), 0<=i,j<=n-1.

Example

In size 1, the scheme {x^2=0} is of degree 2. in size 2, the scheme of matrices {{m11,m12},{m21,m22}} that square to zero is generically reduced and the corresponding reduced scheme is given by the equations m11+m22=0 and m11^2+m12 m21=0, hence also of degree 2.

Mathematica

a[1] = 2; a[n_] := If[EvenQ[n], 2^(n/2) Det[Table[Binomial[2i + 2j + 1, 2i], {i, 0, n/2-1}, {j, 0, n/2-1}]], 2^((n-1)/2+1) Det[Table[Binomial[2i + 2j + 3, 2i + 1], {i, 0, (n-1)/2-1}, {j, 0, (n-1)/2-1}]]];
Array[a, 12] (* Jean-François Alcover, Dec 04 2018 *)

Crossrefs

Cf. A130294.

Sequence in context: A287951 A287629 A324919 * A199127 A093044 A151366

Adjacent sequences: A130303 A130304 A130305 * A130307 A130308 A130309

Keyword

nonn

Author

Paul Zinn-Justin, Aug 06 2007

Extensions

More terms from Alois P. Heinz, Dec 04 2018

Status

approved