A359335 Square root of determinant of skew-symmetric 2n X 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n.

1, 3, 14, 84, 360, 2160, 10080, 60480, 249984, 1499904, 6999552, 41997312, 179988480, 1079930880, 5039677440, 30238064640, 122903101440, 737418608640, 3441286840320, 20647721041920, 88490233036800, 530941398220800, 2477726525030400, 14866359150182400

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..400

Formula

It appears that for n > 1, a(n) / a(n-1) = 2 * (4*e(n)-1) / (2*e(n)-1), where e(n) = A006519(n).

Maple

f:= proc(n) uses LinearAlgebra, MmaTranslator[Mma];
    sqrt(Determinant(Matrix(2*n, 2*n, (i, j) -> signum(i-j)*BitXor(i, j))))
end proc:
f(0):= 1:
map(f, [$0..30]); # Robert Israel, Mar 31 2026

Mathematica

a[0] = 1;
a[n_] := Sqrt@Det@Table[Sign[i - j] BitXor[i, j], {i, 2 n}, {j, 2 n}];
Table[a[n], {n, 0, 20}]

Prog

(PARI) a(n) = sqrtint(matdet(matrix(2*n, 2*n, i, j, sign(i-j)*bitxor(i, j)))); \\ Michel Marcus, Dec 28 2022

Crossrefs

Cf. A006519.

Sequence in context: A121687 A154757 A352307 * A074535 A256337 A256330

Adjacent sequences: A359332 A359333 A359334 * A359336 A359337 A359338

Keyword

nonn

Author

Andrei Zabolotskii, Dec 26 2022

Status

approved