A137774 Number of ways to place n nonattacking empresses on an n X n board.

1, 2, 2, 8, 20, 94, 438, 2766, 19480, 163058, 1546726, 16598282, 197708058, 2586423174, 36769177348, 563504645310, 9248221393974, 161670971937362, 2996936692836754, 58689061747521430, 1210222434323163704, 26204614054454840842, 594313769819021397534, 14086979362268860896282

Offset

1,2

Comments

An empress moves like a rook and a knight.

Links

Martin Fuller, Table of n, a(n) for n = 1..30

Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, Separators - a new statistic for permutations, arXiv:1905.12364 [math.CO], 2019.

Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, On the Sparseness of the Downsets of Permutations via Their Number of Separators, Enumerative Combinatorics and Applications (2021) Vol. 1, No. 3, Article #S2R21.

Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p.685 and 636.

Wolfram Schubert, N-Queens page.

Formula

Asymptotics: a(n)/n! -> 1/e^4.

General asymptotic formulas for number of ways to place n nonattacking pieces rook + leaper[r,s] on an n X n board:

a(n)/n! -> 1/e^2 for 0<r=s

a(n)/n! -> 1/e^4 for 0<r<s

Crossrefs

Cf. A201513, A000170, A002465, A201540.

Cf. A185085, A051223, A244284, A201511, A201861, A137774, A245011.

Cf. A218244, A002464, A110128, A117574, A089222, A002493.

Sequence in context: A292476 A348534 A259807 * A167532 A208235 A151377

Adjacent sequences: A137771 A137772 A137773 * A137775 A137776 A137777

Keyword

nonn,nice,hard

Author

Vaclav Kotesovec, Jan 27 2011

Extensions

Terms a(16)-a(17) from Vaclav Kotesovec, Feb 06 2011

Terms a(18)-a(19) from W. Schubert, Jul 24 2011

Terms a(20)-a(24) (computed by W. Schubert), Vaclav Kotesovec, Aug 25 2012

Status

approved