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A117574 Total number of permutations p of [n] such that |p(i+3) - p(i)| is not equal to 3 for 1 <= i <= n-3. 8
1, 2, 6, 20, 80, 384, 2240, 15424, 123456, 1110928, 11287232, 127016304, 1565107248, 20935873872, 301974271248, 4669727780624, 77046043259824, 1350585114106416, 25062108668100208, 490725684463001488, 10109820295907492304 (list; graph; refs; listen; history; text; internal format)
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 non-attacking 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

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)