A057507 -id:A057507 - cp's OEIS frontend

A038775 a(n) is the number of cycles of the permutation that converts forest(n) of depth-first planar planted binary trees into breadth-first representation.

1, 2, 3, 6, 10, 12, 17, 26, 34, 50, 56, 68, 82, 94, 113

Offset: 1

Wouter Meeussen, May 04 2000

The first a(n) terms of A038774 add up to Catalan(n) = A000108(n).

			a(5)=10 since there are 10 cycles in this permutation of forest(5), with lengths 1, 1, 3, 4, 3, 2, 16, 8, 2, 2 summing up to 42=Catalan(5).

Sean A. Irvine, Java program (github)

Cf. A000108, A038774.

Similarly generated sequences: A001683, A002995, A003239, A057507, A057513.

a(13)-a(15) from Sean A. Irvine, May 22 2022

A079437 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071661.

Original entry on oeis.org

1, 1, 2, 3, 6, 16, 36, 83, 190, 448, 1056, 2514, 5872, 13806, 32424, 76609, 181434, 432062, 1032716

Offset: 0

Antti Karttunen, Jan 27 2003

That is, number of orbits to which "Catalan bijections" A071661/A071662 partition each A000108(n) Catalan tree structures encoded in A014486[A014137(n-1)..A014138(n-1)].

Antti Karttunen, C-program for counting the initial terms of this sequence

Occurs in A073201 as row 13373289.

Cf. A079438, A079439, A057507, A079441.

A079441 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071663.

Original entry on oeis.org

1, 1, 1, 4, 7, 24, 48, 128, 259, 646, 1426, 3458, 7924, 19054, 44684, 107586, 255971, 617012, 1482096

Offset: 0

Antti Karttunen, Jan 27 2003

That is, number of orbits to which "Catalan bijections" A071663/A071664 partition each A000108(n) Catalan tree structures encoded in A014486[A014137(n-1)..A014138(n-1)].

Antti Karttunen, C-program for counting the initial terms of this sequence

Occurs in A073201 as row 176609070820803.

Cf. A057507, A079437, A079442, A079443.

A081167 Number of cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506.

Original entry on oeis.org

1, 2, 10, 46, 236, 1288, 6984, 38528, 216648, 1240818

Offset: 0

Wouter Meeussen and Antti Karttunen, Mar 10 2003

Cf. A057507, A081151, A014137, A014138, A057505, A057506.

a(n) = A057507(2n+1).

cp's OEIS Frontend

A038775 a(n) is the number of cycles of the permutation that converts forest(n) of depth-first planar planted binary trees into breadth-first representation.

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A079437 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071661.

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A079441 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A071663.

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A081167 Number of cycles in range [A014137(2n)..A014138(2n)] of permutation A057505/A057506.

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