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

Author

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

Keywords

• nonn

References

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

Links

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

Crossrefs

Cf. A002884.

Programs

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 *)

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).

Extensions

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