A189563 Number of permutations p of 1,2,...,n satisfying |p(i+1)-p(i)|<>4 and |p(j+4)-p(j)|<>1 for all i=1..n-1, j=1..n-4.

1, 1, 2, 6, 24, 48, 182, 868, 5752, 37156, 296944, 2738820, 28894206, 335399468, 4285522402, 59536763892, 892785282788, 14347054185602, 245880923199152, 4473839857744204, 86101137756244992, 1746946085050010604, 37260139829836652906, 833279639470464066112

Offset

0,3

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[1,4] on an n X n chessboard (in fairy chess the leaper[1,4] is called a giraffe).

Links

Table of n, a(n) for n=0..23.

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

Formula

Asymptotic: a(n)/n! ~ 1/e^4.

Crossrefs

Cf. A137774, A189358.

Sequence in context: A099144 A354216 A189851 * A321613 A104114 A175624

Adjacent sequences: A189560 A189561 A189562 * A189564 A189565 A189566

Keyword

nonn,hard

Author

Vaclav Kotesovec, Apr 23 2011

Extensions

a(17)-a(23) from Martin Fuller, Mar 21 2026

Status

approved