cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

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.

Original entry on oeis.org

1, 1, 2, 6, 24, 48, 182, 868, 5752, 37156, 296944, 2738820, 28894206, 335399468, 4285522402, 59536763892, 892785282788
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

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

Crossrefs

Cf. A137774, A189358.

Formula

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

A189564 Number of permutations p of 1,2,...,n satisfying |p(i+1)-p(i)|<>5 and |p(j+5)-p(j)|<>1 for all i=1..n-1, j=1..n-5.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 336, 1474, 8340, 57756, 475658, 4171070, 41950294, 472535256, 5882635676, 79963449714, 1173614446044
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[1,5] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563.

Formula

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

A189565 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)|<>3 and |p(j+3)-p(j)|<>2 for all i=1..n-2, j=1..n-3.

Original entry on oeis.org

1, 1, 2, 6, 12, 36, 174, 708, 4334, 31424, 263732, 2503296, 26844578, 316692056, 4090634212, 57274447458, 863488976620
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[2,3] on an n X n chessboard (in fairy chess the leaper [2,3] is called a zebra).

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564.

Formula

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

A189566 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)|<>4 and |p(j+4)-p(j)|<>2 for all i=1..n-2, j=1..n-4.

Original entry on oeis.org

1, 2, 6, 24, 60, 208, 1184, 7840, 51636, 410272, 3836456, 39971896, 455888312, 5717233896, 78164908748, 1153568477544, 18263732340736, 308795344195456, 5550690255143992, 105653899427070440, 2122307518838927952
Offset: 1

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[2,4] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565.

Formula

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

Extensions

a(17)-a(21) from Max Alekseyev, Jul 28 2024

A189567 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)|<>5 and |p(j+5)-p(j)|<>2 for all i=1..n-2, j=1..n-5.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 392, 1810, 10400, 72228, 589674, 5196870, 52398658, 588036216, 7274466172, 98024173852, 1427556373892
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[2,5] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565, A189566.

Formula

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

A189568 Number of permutations p of 1,2,...,n satisfying |p(i+3)-p(i)|<>4 and |p(j+4)-p(j)|<>3 for all i=1..n-3, j=1..n-4.

Original entry on oeis.org

1, 1, 2, 6, 24, 80, 326, 1566, 9544, 65036, 518498, 4750006, 48830634, 554929274, 6926227324, 93970452970, 1377573324202
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[3,4] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565, A189566, A189567.

Formula

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

A189864 Number of ways to place n nonattacking composite pieces queen + leaper[1,3] on an n X n chessboard.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 56, 176, 1932, 4188, 26960, 182456, 1132064, 7645784, 58695136, 470822912, 3792417988, 32440237692
Offset: 1

Views

Author

Vaclav Kotesovec, Apr 29 2011

Keywords

Comments

(In fairy chess, the leaper [1,3] is called a camel.)
a(n) is also the number of permutations p of 1,2,...,n satisfying |p(i+1) - p(i)| <> 3 AND |p(j+3) - p(j)| <> 1 AND |p(m+k) - p(m)| <> k for all i >= 1, j >= 1, m >= 1, k >= 1, i+1 <= n, j+3 <= n, m+k <= n.

Links

Crossrefs

Cf. A051223, A189358.

A189569 Number of permutations p of 1,2,...,n satisfying |p(i+3)-p(i)|<>5 and |p(j+5)-p(j)|<>3 for all i=1..n-3, j=1..n-5.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 464, 2274, 13236, 91760, 740562, 6541984, 65632694, 732880076, 8995905626, 120367234946
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[3,5] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565, A189566, A189567, A189568.

Formula

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

A189570 Number of permutations p of 1,2,...,n satisfying |p(i+4)-p(i)|<>5 and |p(j+5)-p(j)|<>4 for all i=1..n-4, j=1..n-5.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 552, 2826, 17080, 117816, 943250, 8330356, 82954582, 915854808, 11147075946, 147948526182
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[4,5] on an n X n chessboard.

Links

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565, A189566, A189567, A189568, A189569.

Formula

Asymptotic: a(n)/n! ~ 1/e^4.
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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