

A117574


Total number of permutations p of [n] such that p(i+3)  p(i) is not equal to 3 for 1 <= i <= n3.


8



1, 2, 6, 20, 80, 384, 2240, 15424, 123456, 1110928, 11287232, 127016304, 1565107248, 20935873872, 301974271248, 4669727780624, 77046043259824, 1350585114106416, 25062108668100208, 490725684463001488, 10109820295907492304
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OFFSET

1,2


COMMENTS

a(n) is also number of ways to place n nonattacking pieces rook + leaper[3,3] on an n X n chessboard.


REFERENCES

Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, vol. 6 (2006), paper A11.


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..30
V. Kotesovec, Number of ways of placing nonattacking queens, kings, bishops and knights (in English and Czech)
Vaclav Kotesovec, Mathematica program for this sequence


FORMULA

Formula given in Tauraso reference.
Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 8/n + 30/n^2)/e^2.


CROSSREFS

Cf. A002464, A110128.
Sequence in context: A245373 A204440 A189839 * A177481 A177475 A118476
Adjacent sequences: A117571 A117572 A117573 * A117575 A117576 A117577


KEYWORD

nonn,hard


AUTHOR

James A. Sellers, Apr 27 2006


EXTENSIONS

Terms a(17)a(28) from Vaclav Kotesovec, Apr 19 2011
Terms a(29)a(30) from Vaclav Kotesovec, Apr 20 2012


STATUS

approved



