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A137774 Number of ways to place n nonattacking empresses on an n X n board. 13
1, 2, 2, 8, 20, 94, 438, 2766, 19480, 163058, 1546726, 16598282, 197708058, 2586423174, 36769177348, 563504645310, 9248221393974, 161670971937362, 2996936692836754, 58689061747521430, 1210222434323163704, 26204614054454840842, 594313769819021397534, 14086979362268860896282 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An empress moves like a rook and a knight.

LINKS

Table of n, a(n) for n=1..24.

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

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

W. Schubert, N-Queens page

FORMULA

Asymptotics (Vaclav Kotesovec, Jan 26 2011): 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: A178076 A292476 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 Wolfram Schubert, Jul 24 2011

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

STATUS

approved

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Last modified June 18 06:02 EDT 2021. Contains 345098 sequences. (Running on oeis4.)