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.

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A081151 Number of even cycles in range [A014137(2n-1)..A014138(2n-1)] of permutation A057505/A057506.

Original entry on oeis.org

0, 1, 3, 18, 95, 528, 2936, 16212, 90717, 516358, 2979992
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

Equal to the number of all cycles in the same range (after n>0).

Crossrefs

Cf. A081152.
Cf. A081150, A081158, A001700, A057507.
Cf. A014137, A014138, A057505, A057506.

Formula

a(n) = A081150(2n) = A081158(n)+A001700(n-1) [where A001700(-1) is taken as 0 here] = A057507(2n) [After n>0].

A081157 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with no fixed points of either A057163 or A057164.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 8, 20, 60, 148, 402, 986, 2474, 5918, 14496, 34708, 84282, 202664, 492048
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A014137, A014138, A057505, A057506, A057163, A057164
Bisections: A081158, A081159. Cf. A081150, A081160, A081162.

A081160 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with two fixed-points of A057164.

Original entry on oeis.org

0, 0, 1, 1, 3, 4, 10, 16, 35, 60, 126, 225, 462, 848, 1716, 3188, 6435, 12095, 24310
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Bisections: A001700 (shifted right and prepended with zero) and A081161.
Cf. A081150, A081157, A081162.
Cf. A014137, A014138, A057505, A057506, A057164.

A081162 Number of even cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with two fixed-points of A057163.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 15, 0, 56, 0, 185, 0, 655, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

Because A057163 can fix only binary trees of odd size, the even-indexed terms are all 0.

Crossrefs

Bisection: A081163. Cf. A081150, A081157, A081160.
Cf. A014137, A014138, A057505, A057506, A057163.

A081153 Number of odd cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with no fixed points of either A057163 or A057164.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 0, 6, 0, 18, 0, 50, 0, 142, 0, 388, 0, 1114, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen Mar 10 2003

Keywords

Crossrefs

Bisection: A081154.
Cf. A081148, A081155.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081148(n)-A081155(n).

A081155 Number of odd cycles in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506, with fixed-points of both A057163 and A057164.

Original entry on oeis.org

1, 1, 0, 1, 0, 2, 0, 3, 0, 6, 0, 12, 0, 20, 0, 59, 0, 120, 0
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

See comment at A080973. Because A057163 can fix only binary trees of odd size, the even-indexed terms are all 0 after n>0.

Crossrefs

Bisection: A081156.
Cf. A081148, A081153.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081148(n)-A081153(n).

A081163 Number of even cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with two fixed-points of A057163.

Original entry on oeis.org

0, 0, 0, 1, 4, 15, 56, 185, 655
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081162, A000108, A081156.
Cf. A014137, A014138, A057505, A057506, A057163.

Formula

a(n) = A081162(2n+1) = (A000108(n) - A081156(n))/2.

A081164 Number of distinct cycle lengths in range [A014137(n-1)..A014138(n-1)] of permutation A057505/A057506.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 4, 11, 15, 25, 32, 64, 88, 155, 234, 423, 647, 1184, 1800
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Comments

This is the number of nonzero, non-constant terms of the polynomials M_n(x) Donaghey gives on the page 81 of his paper. The term x^18 seems to have been accidentally dropped from the polynomial M_7(x).

Links

Crossrefs

Cf. A081166, A060114.

A081152 Number of even cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506.

Original entry on oeis.org

0, 1, 6, 37, 212, 1226, 6822, 38081, 215414
Offset: 0

Views

Author

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Keywords

Crossrefs

Cf. A081151.
Cf. A081150, A081159, A081161, A081163.
Cf. A014137, A014138, A057505, A057506.

Formula

a(n) = A081150(2n+1) = A081159(n)+A081161(n)+A081163(n).

A081156 Number of odd cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506, with fixed-points of both A057163 and A057164.

Original entry on oeis.org

1, 1, 2, 3, 6, 12, 20, 59, 120
Offset: 0

Views

Author

Wouter Meeussen & Antti Karttunen Mar 10 2003

Keywords

Comments

See comment at A080973.

Crossrefs

Cf. A080973.
Cf. A081155, A000108, A081163.
Cf. A014137, A014138, A057505, A057506, A057163, A057164.

Formula

a(n) = A081155(2n+1) = A000108(n) - 2*A081163(n).
Previous Showing 11-20 of 40 results. Next

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