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 1-10 of 40 results. Next

A057507 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

1, 1, 1, 2, 3, 10, 18, 46, 95, 236, 528, 1288, 2936, 6984, 16212, 38528, 90717, 216648, 516358, 1240818, 2979992
Offset: 0

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Author

Antti Karttunen, Sep 03 2000

Keywords

Comments

For the convenience of the range notation above, we define A014137(-1) and A014138(-1) as zero.

Links

Crossrefs

a(n) = A081148(n)+A081150(n). Bisections: A081151, A081167. Cf. A057545, A060114, A081164.
Occurs for first time in A073201 as row 2614.

A071666 Permutation A057506 applied four times ("^4"), permutation A071662 squared.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 11, 19, 17, 20, 12, 10, 15, 21, 18, 13, 22, 23, 37, 42, 28, 51, 44, 53, 30, 25, 39, 56, 48, 33, 60, 45, 54, 57, 34, 61, 31, 40, 26, 24, 38, 43, 47, 29, 52, 58, 62, 49, 46, 55, 35, 32, 27, 41, 63, 59, 50, 36, 64, 65, 107, 121, 79, 149, 126
Offset: 0

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Author

Antti Karttunen, May 30 2002

Keywords

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Crossrefs

Inverse permutation: A071665 and also its car/cdr-flipped conjugate, i.e. A071666(n) = A057163(A071665(A057163(n))) = A057506(A071664(n)) = A071662(A071662(n)). Cf. also A071662, A071668, A071670.

A071662 Permutation A057506 applied twice ("squared").

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 12, 16, 21, 10, 18, 11, 14, 20, 13, 15, 19, 22, 23, 45, 31, 44, 58, 26, 49, 30, 42, 57, 35, 43, 56, 63, 24, 46, 32, 47, 59, 25, 48, 28, 37, 54, 34, 40, 53, 62, 27, 50, 29, 38, 55, 33, 39, 51, 61, 36, 41, 52, 60, 64, 65, 129, 87, 128, 170, 73
Offset: 0

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Author

Antti Karttunen, May 30 2002

Keywords

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Crossrefs

Inverse permutation: A071661 and also its car/cdr-flipped conjugate, i.e. A071662(n) = A057163(A071661(A057163(n))) = A057506(A057506(n)). Cf. also A071664, A071666, A071668, A071670.

A071668 Permutation A057506 applied five times ("^5").

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 6, 4, 22, 21, 18, 20, 17, 13, 12, 15, 19, 16, 10, 11, 14, 9, 64, 63, 59, 62, 58, 50, 49, 55, 61, 57, 46, 34, 54, 45, 36, 35, 32, 40, 31, 41, 43, 52, 60, 56, 47, 48, 53, 44, 27, 26, 29, 33, 30, 38, 39, 51, 42, 24, 25, 28, 37, 23, 196, 195, 190, 194, 189
Offset: 0

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Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071667 and also its car/cdr-flipped conjugate, i.e. A071668(n) = A057163(A071667(A057163(n))) = A057506(A071666(n)). Cf. also A071662, A071664, A071670.

A071664 Permutation A057506 applied three times ("cubed").

Original entry on oeis.org

0, 1, 3, 2, 8, 5, 6, 7, 4, 22, 13, 15, 18, 10, 19, 11, 20, 21, 12, 14, 16, 17, 9, 64, 36, 41, 50, 27, 52, 29, 55, 59, 32, 38, 47, 46, 24, 60, 33, 39, 48, 25, 61, 34, 62, 63, 35, 40, 43, 49, 26, 51, 28, 53, 56, 30, 54, 57, 58, 31, 37, 42, 44, 45, 23, 196, 106, 120, 148, 78
Offset: 0

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071663 and also its car/cdr-flipped conjugate, i.e. A071664(n) = A057163(A071663(A057163(n))) = A057506(A071662(n)). Cf. also A071666, A071668, A071670.

A057545 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

1, 1, 2, 3, 6, 6, 24, 72, 144, 147, 588, 672, 2136, 10152, 11520, 29484, 117936, 270576, 656352, 2062368, 4040160
Offset: 0

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Author

Antti Karttunen, Sep 07 2000

Keywords

Comments

For the convenience of the range notation above, we define A014137(-1) and A014138(-1) as zero.
Equal to the degree of the polynomials M_n(x) Donaghey gives on the page 81 of his paper.
Factored terms: 1, 1, 2, 3, 2*3, 2*3, 2^3 * 3, 2^3 * 3^2, 2^4 * 3^2, 3 * 7^2, 2^2 * 3 * 7^2, 2^5 * 3 * 7, 2^3 * 3 * 89, 2^3 * 3^3 * 47, 2^8 * 3^2 * 5, 2^2 * 3^4 * 7 * 13, 2^4 * 3^4 * 7 * 13, 2^4 * 3^2 * 1879, 2^5 * 3^2 * 43 * 53, 2^5 * 3^3 * 7 * 11 * 31, 2^5 * 3 * 5 * 19 * 443

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Crossrefs

Cf. A057507, A060114, A080967, A081165.
Occurs for first time in A073203 as row 2614.

A060114 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

1, 1, 2, 6, 6, 30, 120, 720, 15120, 1164240, 15135120, 283931716867999200, 14510088480716327580681600, 3280681990411073806237542217555200, 936436634805345771521186435213604447980767985241556128000
Offset: 0

Views

Author

Antti Karttunen, Mar 01 2001

Keywords

Comments

For the convenience of the range notation above, we define A014137(-1) and A014138(-1) as zero.
This sequence grows so fast that it seems hopeless to count A057507 with Burnside's (orbit-counting) lemma.

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Crossrefs

Cf. A057505, A057507, A057545, A081165, A081166, A078491.
Occurs for first time in A073204 as row 2614.

A071670 Permutation A057506 applied six times ("^6"), permutation A071662 cubed, permutation A071664 squared.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 40, 35, 36, 37, 38, 39, 43, 41, 42, 47, 44, 45, 46, 48, 34, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
Offset: 0

Views

Author

Antti Karttunen, May 30 2002

Keywords

Links

Crossrefs

Inverse permutation: A071669 and also its car/cdr-flipped conjugate, i.e. A071670(n) = A057163(A071669(A057163(n))) = A057506(A071668(n)) = A071662(A071662(A071662(n))) = A071664(A071664(n)). Cf. also A071666.

A081150 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

0, 0, 1, 1, 3, 6, 18, 37, 95, 212, 528, 1226, 2936, 6822, 16212, 38081, 90717, 215414, 516358
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

For the convenience of the range notation above, we define A014137(-1) and A014138(-1) as zero.

Links

Crossrefs

Bisections: A081151, A081152.
Cf. A081157, A081160, A081162, A057507, A081148.
Cf. A014137, A014138, A057505, A057506.

Formula

a(n) = A081157(n) + A081160(n) + A081162(n) = A057507(n) - A081148(n).

A081148 Number of odd cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

1, 1, 0, 1, 0, 4, 0, 9, 0, 24, 0, 62, 0, 162, 0, 447, 0, 1234, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

For the convenience of the range notation above, we define A014137(-1) and A014138(-1) as zero.

Links

Crossrefs

Bisection: A081149.
Cf. A081153, A081155, A057507, A081150.
Cf. A014137, A014138, A057505, A057506.

Formula

a(n) = A081153(n) + A081155(n) = A057507(n) - A081150(n).
Showing 1-10 of 40 results. Next

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