A086812 - OEIS

%I #17 Feb 24 2019 12:32:17

%S 1,4,28,448,13888,888832,112881664,28897705984,14766727757824,

%T 15121129224011776,30952951521552105472,126783289432277424013312,

%U 1038481923739784380093038592,17014487838552627283444344291328

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

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

%H R. P. Brent and B. D. McKay, <a href="https://arxiv.org/abs/1004.5440">Determinants of random symmetric matrices over Zm</a>, arXiv:1004.5440 [math.CO], 2010.

%F 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).

%p 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

%t 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}]];

%t Array[a, m] (* _Jean-François Alcover_, Feb 24 2019, from Maple *)

%Y Cf. A002884.

%K nonn

%O 1,2

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

%E More terms from _Ray Chandler_ and _Sascha Kurz_, Sep 19 2003