login
A103869
Number of unlabeled graphs with n nodes whose adjacency matrix has nonzero even determinant.
1
0, 0, 1, 0, 9, 10, 354, 1752, 141494, 3313095, 728952205
OFFSET
1,5
FORMULA
a(n) = A140981(n) - A133206(n).
For odd n, a(n) = A109717(n). For even n, a(n) = A109717(n) - A141040(n/2). - Max Alekseyev, Feb 20 2024
MATHEMATICA
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
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Tanya Khovanova, Aug 29 2008
EXTENSIONS
a(8)-a(10) from Andrew Howroyd, Nov 04 2017
a(11) from A109717 added by Max Alekseyev, Feb 20 2024
STATUS
approved