A072659 -id:A072659 - cp's OEIS frontend

A072660 Size of the parenthesizations obtained with the global ranking/unranking scheme A072656-A072659.

0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 5, 4, 4, 4, 5, 4, 4, 6, 5, 5, 5, 5, 4, 6, 5, 4, 4, 5, 7, 6, 6, 6, 5, 5, 5, 6, 5, 5, 7, 6, 6, 6, 5, 4, 6, 5, 8, 7, 7, 7, 6, 7, 6, 6, 6, 6, 5, 7, 6, 5, 4, 6, 8, 7, 7, 7, 6, 6, 5, 7, 5, 5, 8, 6, 6, 9, 8, 8, 8, 7, 8, 7, 7, 9, 7, 7, 7, 6, 6, 5, 7, 5, 6, 8, 7, 7, 6, 6, 4, 7, 5, 9, 8

Offset: 0

Antti Karttunen, Jun 02 2002

nonn

Cf. A072657-A072659. Permutations: A071673, A072643, A072644, A072645.

A072657 Inverse permutation to A072656.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 5, 7, 19, 22, 15, 4, 52, 16, 13, 20, 60, 18, 14, 178, 43, 51, 61, 41, 11, 153, 53, 10, 21, 47, 555, 155, 177, 136, 42, 33, 64, 179, 55, 39, 557, 125, 151, 181, 38, 12, 150, 56, 1799, 479, 553, 417, 154, 552, 164, 135, 192, 117, 36, 471, 191, 29, 17

Offset: 0

Antti Karttunen, Jun 02 2002

nonn

A. Karttunen, Gatomorphisms (With the complete source)
Index entries for sequences that are permutations of the natural numbers

A072657(n) = A057163(A072659(n)). A072660 gives the size of the corresponding parenthesizations, i.e. A072660(n) = A029837(A014486(A072657(n))+1)/2 [A029837(n+1) gives the binary width of n].

A072658 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238tr as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 11, 9, 28, 15, 17, 62, 8, 13, 10, 14, 45, 18, 24, 27, 100, 36, 187, 117, 91, 1292, 22, 70, 38, 72, 680, 93, 111, 295, 1229, 16, 47, 26, 29, 102, 12, 20, 23, 58, 302, 73, 189, 147, 2090, 21, 34, 39, 35, 113, 44, 61, 116, 1100, 162, 150, 179, 477

Offset: 0

Antti Karttunen, Jun 02 2002

nonn

A. Karttunen, Gatomorphisms
Index entries for sequences that are permutations of the natural numbers

Inverse permutation: A072659. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072656, A072660.

A072661 Composition of the A059905 and A048679, i.e., a(n) = A059905(A048679(n)).

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 2, 4, 1, 0, 2, 3, 0, 5, 4, 6, 1, 4, 3, 2, 8, 1, 0, 2, 5, 0, 7, 6, 4, 5, 4, 6, 3, 0, 9, 8, 10, 1, 8, 3, 2, 12, 1, 0, 2, 7, 8, 5, 4, 6, 5, 4, 7, 6, 16, 1, 0, 2, 9, 0, 11, 10, 4, 9, 8, 10, 3, 0, 13, 12, 14, 1, 12, 3, 2, 8, 9, 8, 10, 5, 8, 7, 6, 12, 5, 4, 6, 7, 0, 17, 16, 18, 1, 16, 3, 2

Offset: 0

Antti Karttunen, Jun 02 2002

nonn

The other side of this projection is A072662. Used to construct the permutations A072657 and A072659.

A072662 Composition of the A059906 and A048679, i.e., a(n) = A059906(A048679(n)).

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 3, 2, 1, 4, 0, 1, 0, 3, 2, 2, 3, 0, 4, 5, 4, 1, 6, 0, 1, 4, 2, 3, 2, 3, 8, 0, 1, 0, 5, 2, 4, 5, 0, 6, 7, 6, 1, 4, 4, 5, 4, 3, 6, 2, 3, 0, 8, 9, 8, 1, 10, 0, 1, 8, 2, 3, 2, 5, 12, 0, 1, 0, 7, 2, 6, 7, 8, 4, 5, 4, 5, 6, 4, 5, 4, 6, 7, 6, 3, 16, 0, 1, 0, 9, 2, 8, 9, 0, 10, 11, 10, 1

Offset: 0

Antti Karttunen, Jun 02 2002

nonn

The other side of this projection is A072661. Used to construct the permutations A072657 and A072659.

cp's OEIS Frontend

A072660 Size of the parenthesizations obtained with the global ranking/unranking scheme A072656-A072659.

Views

Author

Keywords

Crossrefs

A072657 Inverse permutation to A072656.

Views

Author

Keywords

Links

Crossrefs

A072658 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238tr as the packing bijection N X N -> N.

Views

Author

Keywords

Links

Crossrefs

A072661 Composition of the A059905 and A048679, i.e., a(n) = A059905(A048679(n)).

Views

Author

Keywords

Crossrefs

A072662 Composition of the A059906 and A048679, i.e., a(n) = A059906(A048679(n)).

Views

Author

Keywords

Crossrefs