A088672 Number of n X n (0,1)-matrices with zero permanent.

0, 1, 9, 265, 27713, 10363361, 13906734081, 68121583929729

Offset: 0

Author

Michael Somos, Oct 03 2003

Keywords

• nonn
• more
• hard

Links

• C. J. Everett and P. R. Stein, The asymptotic number of (0,1)-matrices with zero permanent, Disc. Math. 6 (1973), 29-34.
• Index entries for sequences related to binary matrices

Crossrefs

Cf. A089479, A089482, A227414.

Programs

Mathematica

a[ n_] := Count[Table[Permanent[Partition[a, n]], {a, Tuples[{0, 1}, n^2]}], 0]; (* Michael Somos, Aug 05 2018 *)

Formula

a(n) is asymptotic to n*(2^(n^2 - n + 1)). [Everett and Stein]

a(n) = A002416(n) - A227414(n). - Geoffrey Critzer, Dec 19 2023

Extensions

a(5) from Jaap Spies, Nov 02 2003

a(6) from Gordon F. Royle, Nov 03 2003

a(7) added by Geoffrey Critzer, Dec 19 2023 after Noam Zeilberger in A227414.

a(0)=0 prepended by Alois P. Heinz, Dec 19 2023