A051236 Largest integer a(n) for which the integer interval [ 0,a(n) ] is a subset of the set of determinants of all n X n 0-1 matrices.

1, 1, 2, 3, 5, 9, 18, 40, 102, 268

Offset: 1

Author

Gerhard R. Paseman (paseman(AT)prado.com)

Keywords

• hard
• nice
• nonn

Comments

A definition for a(n) is given in Craigen's paper. The table given there suggests a(9)=102. Term for term, this sequence is one less than the sequence A013588.

Examples

			There is a 7x7 0-1 matrix with determinant 20, but no 7x7 0-1 matrix with determinant 19.
		

References

• R. Craigen, The Range of the Determinant Function on the Set of n X n (0,1)-Matrices, J. Combin. Math. Combin. Computing, 8 (1990) pp. 161-171.

Links

• G. R. Paseman, A Different Approach to Hadamard's Maximum Determinant Problem

Crossrefs

Cf. A013588.

Formula

a(n) = A013588(n) - 1

Extensions

Extended by William Orrick, Jan 12 2006