A215897 a(n) = A215723(n) / 2^(n-1).

1, 0, 1, 2, 3, 4, 8, 18, 27, 44, 267, 1024, 3645, 6144, 23859, 50176, 187377, 531468, 3302697, 10616832, 39337984, 102546588, 568833245, 3073593600, 8721488875, 32998447572, 164855413835, 572108938470, 2490252810073, 10831449635712, 68045615234375, 282773291271138, 1592413932070703, 5234078743146888

Offset: 1

Author

Joerg Arndt, Aug 26 2012

Keywords

• nonn
• hard

Comments

A215723(n) is divisible by 2^(n-1), indeed the determinant of any n X n sign matrix is divisible by 2^(n-1). Proof: subtract the first row from other rows, the result is all rows except for the first are divisible by 2, hence by using expansion by minors proof follows. (Warren D. Smith on the math-fun mailing list, Aug 18 2012)

Links

• Richard P. Brent, Table of n, a(n) for n = 1..52
• Richard P. Brent and Adam B. Yedidia, Computation of maximal determinants of binary circulant matrices, arXiv:1801.00399 [math.CO], 2018.
• R. P. Brent and A. Yedidia, Computation of maximal determinants of binary circulant matrices, Journal of Integer Sequences, 21 (2018), article 18.5.6.
• Index entries for sequences related to maximal determinants

Crossrefs

Cf. A215723 (Maximum determinant of an n X n circulant (1,-1)-matrix).

Formula

a(n) = A215723(n) / 2^(n-1).

Extensions

a(23)-a(28) (as calculated by Warren Smith) from W. Edwin Clark, Sep 02 2012

a(29) onward from Richard P. Brent, Jan 02 2018