A306837 -id:A306837

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A363862

Number of equivalence classes of unimodular n X n matrices with elements {0, 1}.

+10
2

1, 2, 7, 49, 831, 39637, 5593528, 2363927011

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

An integer matrix is unimodular if its determinant is -1 or +1. Two matrices are equivalent if one can be obtained from the other by permuting rows and columns.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

For n=1, the only example is [1]. For n=2, representatives of the equivalence classes are [[1,0],[0,1]] and [[1,1],[0,1]].

CROSSREFS

A306837 gives the total counts rather than equivalence classes.

KEYWORD

nonn,hard,more

AUTHOR

Brendan McKay, Jun 25 2023

STATUS

approved

A363884

Number of connected bipartite graphs on 2n nodes with a distinguished partite set of size n and with a unimodular reduced adjacency matrix.

+10
0

1, 1, 5, 41, 777, 38749, 5552904, 2358289931

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..8.

CROSSREFS

Inverse Euler transform of A363862.

Cf. A306837, A363846.

KEYWORD

nonn,more,hard

AUTHOR

Max Alekseyev, Jun 25 2023

STATUS

approved

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