A189282 -id:A189282 - cp's OEIS frontend

A189283 Number of permutations p of 1,2,...,n satisfying p(i+4)-p(i)<>4 for all 1<=i<=n-4.

1, 1, 2, 6, 24, 114, 628, 4062, 30360, 255186, 2414292, 25350954, 292378968, 3673917102, 49928069188, 729534877758, 11403682481112, 189862332575658, 3354017704180052, 62654508729565554, 1233924707891272728, 25550498290562247438

Offset: 0

Vaclav Kotesovec, Apr 19 2011

a(n) is also number of ways to place n nonattacking pieces rook + semi-leaper[4,4] on an n X n chessboard.

Vaclav Kotesovec, Table of n, a(n) for n = 0..27 (Updated Jan 19 2019)
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 644.
Vaclav Kotesovec, Mathematica program for this sequence
George Spahn and Doron Zeilberger, Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s), arXiv:2211.02550 [math.CO], 2022.

Cf. A000255, A189281, A189282, A189255.

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 7/n + 12/n^2)/e.

Terms a(26)-a(27) from Vaclav Kotesovec, Apr 20 2012

A189284 Number of permutations p of 1,2,...,n satisfying p(i+5)-p(i)<>5 for all 1<=i<=n-5.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 696, 4572, 34260, 290328, 2751480, 28686024, 328764732, 4106158164, 55495145304, 806797105320, 12554890849992, 208164423163908, 3663256621120548, 68188490015132040, 1338490745511631080, 27630826605742438968

Offset: 0

Vaclav Kotesovec, Apr 19 2011

a(n) is also number of ways to place n nonattacking pieces rook + semi-leaper[5,5] on an n X n chessboard.

Vaclav Kotesovec, Table of n, a(n) for n = 0..26 (Updated Jan 19 2019)
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 644.
Vaclav Kotesovec, Mathematica program for this sequence
George Spahn and Doron Zeilberger, Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s), arXiv:2211.02550 [math.CO], 2022.

Cf. A000255, A189281, A189282, A189283, A189256.

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 9/n + 20/n^2)/e.

Terms a(25)-a(26) from Vaclav Kotesovec, Apr 20 2012

A189844 Number of ways to place n nonattacking composite pieces rook + semi-rider[3,3] on an n X n chessboard.

Original entry on oeis.org

1, 2, 6, 22, 98, 534, 3334, 23724, 191820, 1704532, 16689868, 179288892, 2069311996, 25760882744, 345073745880, 4900331447624

Offset: 1

Vaclav Kotesovec, Apr 29 2011

a(n) is also number of permutations p of 1,2,...,n satisfying p(j+3k)-p(j)<>3k for all j>=1, k>=1, j+3k<=n.

For information about semi-pieces see semi-bishop (A187235) and semi-queen (A099152).

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

Cf. A189282, A099152, A189843, A189839, A187235

A189285 Number of permutations p of 1,2,...,n satisfying p(i+6)-p(i)<>6 for all 1<=i<=n-6.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4920, 37488, 319644, 3033264, 31784280, 364902480, 4538652840, 61102571376, 885045657564, 13722397569072, 226742901078120, 3977354871110160, 73816786920489720, 1444940702597713008, 29750236302549282948

Offset: 0

Vaclav Kotesovec, Apr 19 2011

a(n) is also number of ways to place n nonattacking pieces rook + semi-leaper[6,6] on an n X n chessboard.

Vaclav Kotesovec, Table of n, a(n) for n = 0..24 (Updated Jan 19 2019)
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 644.
Vaclav Kotesovec, Mathematica program for this sequence
George Spahn and Doron Zeilberger, Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s), arXiv:2211.02550 [math.CO], 2022.

Cf. A000255, A189281, A189282, A189283, A189284, A189271.

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 11/n + 30/n^2)/e.

Generally (for this sequence is d=6): 1/e*(1+(2d-1)/n+d*(d-1)/n^2).

Terms a(23)-a(24) from Vaclav Kotesovec, Apr 21 2012

cp's OEIS Frontend

A189283 Number of permutations p of 1,2,...,n satisfying p(i+4)-p(i)<>4 for all 1<=i<=n-4.

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A189284 Number of permutations p of 1,2,...,n satisfying p(i+5)-p(i)<>5 for all 1<=i<=n-5.

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A189844 Number of ways to place n nonattacking composite pieces rook + semi-rider[3,3] on an n X n chessboard.

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A189285 Number of permutations p of 1,2,...,n satisfying p(i+6)-p(i)<>6 for all 1<=i<=n-6.

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