%I #12 Feb 21 2024 01:19:29
%S 0,0,1,0,9,10,354,1752,141494,3313095,728952205
%N Number of unlabeled graphs with n nodes whose adjacency matrix has nonzero even determinant.
%F a(n) = A140981(n) - A133206(n).
%F For odd n, a(n) = A109717(n). For even n, a(n) = A109717(n) - A141040(n/2). - _Max Alekseyev_, Feb 20 2024
%t k = {}; For[i = 1, i < 8, i++, lg = ListGraphs[i] ; len = Length[lg]; k = Append[k, Length[Select[Range[len], Det[ToAdjacencyMatrix[lg[[ # ]]]] != 0 && Mod[Det[ToAdjacencyMatrix[lg[[ # ]]]], 2] == 0 &]]]]; k
%Y Cf. A133206, A140981, A141040, A109717, A000088.
%K more,nonn
%O 1,5
%A _Tanya Khovanova_, Aug 29 2008
%E a(8)-a(10) from _Andrew Howroyd_, Nov 04 2017
%E a(11) from A109717 added by _Max Alekseyev_, Feb 20 2024