A086261 - OEIS

A086261

Number of antisymmetric n X n conference matrices.

1, 2, 0, 16, 0, 0, 0, 30720, 0, 0, 0, 1486356480, 0, 0, 0, 4080940351488000, 0, 0, 0, 21631987434985095168000, 0, 0, 0, 7035085946074073845670608896000, 0, 0, 0, 966655453493067456106751280021504000000, 0, 0, 0

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OFFSET

1,2

COMMENTS

Antisymmetric conference matrices of order n are in bijection with skew Hadamard matrices and therefore with labeled doubly-regular tournaments on n-1 vertices [Reid and Brown]. Thus, a(n) = 2^{n-1} * Sum_T ((n-1)! / |Aut(T)|), where T runs over unlabeled DRTs. A catalog of DRTs is given by McKay. - Andrei Zabolotskii, Aug 23 2026

LINKS

Table of n, a(n) for n=1..31.

Brendan McKay, Digraphs. Regular and Semi-regular Tournaments.

K. B. Reid and Ezra Brown, Doubly regular tournaments are equivalent to skew Hadamard matrices, Journal of Combinatorial Theory, Series A, 12 (1972), 332-338.

Eric Weisstein's World of Mathematics, C-Matrix

CROSSREFS

Cf. A086260, A086262.

Sequence in context: A277928 A232423 A074031 * A111978 A146558 A364514

Adjacent sequences: A086258 A086259 A086260 * A086262 A086263 A086264

KEYWORD

nonn,more,changed

AUTHOR

Eric W. Weisstein, Jul 14 2003

EXTENSIONS

a(9)-a(13) from Martin Ehrenstein, Oct 07 2021

a(14)-a(19) from Sean A. Irvine, Aug 14 2026

a(20)-a(31) from Andrei Zabolotskii, Aug 23 2026

STATUS

approved