A086812 Number of symmetric invertible n X n matrices over GF(2).

1, 4, 28, 448, 13888, 888832, 112881664, 28897705984, 14766727757824, 15121129224011776, 30952951521552105472, 126783289432277424013312, 1038481923739784380093038592, 17014487838552627283444344291328

Offset

1,2

References

R. P. Brent and B. D. McKay, Determinants of random symmetric matrices over Zm, Ars Combinatoria, 26-A (1988) 57-64.

Links

Table of n, a(n) for n=1..14.

R. P. Brent and B. D. McKay, Determinants of random symmetric matrices over Zm, arXiv:1004.5440 [math.CO], 2010.

Formula

Let k = ceiling(n/2). Then a(n) = 2^(n*(n+1)/2) * (Product_{j=1..2k} (1 - (1/2)^j)) / Product_{j=1..k} (1 - (1/4)^j).

Maple

for n from 1 to 31 do k := ceil(n/2); a[n] := 2^(n*(n+1)/2)*product(1-(1/2)^j, j=1..2*k)/product(1-(1/4)^j, j=1..k); od:seq(a[j], j=1..31); # Sascha Kurz, Sep 19 2003

Mathematica

m = 14; For[n = 1, n <= m, n++, k = Ceiling[n/2]; a[n] = 2^(n*(n+1)/2)* Product[1-(1/2)^j, {j, 1, 2k}]/Product[1-(1/4)^j, {j, 1, k}]];
Array[a, m] (* Jean-François Alcover, Feb 24 2019, from Maple *)

Crossrefs

Cf. A002884.

Sequence in context: A132685 A180966 A203032 * A197872 A203220 A338816

Adjacent sequences: A086809 A086810 A086811 * A086813 A086814 A086815

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 15 2003

Extensions

More terms from Ray Chandler and Sascha Kurz, Sep 19 2003

Status

approved