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 1-6 of 6 results.

A072645 Size of the parenthesizations obtained with the global ranking/unranking scheme A072646/A072647.

Original entry on oeis.org

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

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Author

Antti Karttunen, Jun 02 2002

Keywords

Crossrefs

Each value v occurs A000108(v) times. The maximum position for value v to occur is A072654(v). Permutations: A071673, A072643, A072644, A072660.

A072634 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using A054238 as the pairing function N X N -> N.

Original entry on oeis.org

0, 1, 3, 2, 11, 9, 4, 6, 5, 139, 131, 33, 41, 35, 12, 10, 8, 70, 66, 7, 17, 21, 18, 32907, 32779, 2051, 2179, 2059, 161, 137, 129, 8233, 8201, 43, 515, 547, 521, 140, 132, 34, 42, 36, 16, 14, 72, 16454, 16390, 68, 1026, 1090, 1030, 15, 13, 19, 81, 69, 23, 65
Offset: 0

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Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072635.
Cf. A014486, A000695, A054238, A071651, A072636, A072646, A072656, A072658, A072644.
Cf. also A296689.

Programs

  • Scheme
    ;; Functions below show the essential idea:
(define A072634 (lexrank->arithrank-bijection packA054238))
(define (lexrank->arithrank-bijection packfun) (lambda (n) (rank-bintree (binexp->parenthesization (A014486 n)) packfun)))
(define (rank-bintree bt packfun) (cond ((not (pair? bt)) 0) (else (1+ (packfun (rank-bintree (car bt) packfun) (rank-bintree (cdr bt) packfun))))))
(define (packA054238 x y) (+ (A000695 x) (* 2 (A000695 y))))

A072637 Inverse permutation to A072636.

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 5, 14, 15, 7, 16, 8, 19, 42, 43, 51, 52, 11, 9, 39, 37, 10, 28, 38, 112, 123, 121, 151, 149, 122, 376, 150, 466, 20, 53, 17, 44, 154, 155, 126, 127, 18, 47, 54, 156, 135, 136, 480, 481, 477, 475, 387, 385, 476, 1531, 386, 1234, 415, 413, 1542, 1540
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

A072644 gives the size of the corresponding parenthesizations, i.e. A072644(n) = A029837(A014486(A072637(n))+1)/2 [A029837(n+1) gives the binary width of n].
A072637(n) = A057163(A072635(n)). Cf. also A014486, A059905, A059906, A071654, A072646.

A072656 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA048680oA054238 as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 3, 2, 11, 6, 5, 7, 4, 100, 27, 24, 45, 14, 18, 10, 13, 62, 17, 8, 15, 28, 9, 1988, 477, 179, 1100, 116, 150, 61, 113, 2090, 147, 35, 189, 302, 58, 162, 44, 39, 73, 23, 34, 20, 102, 1229, 295, 29, 111, 680, 72, 21, 12, 26, 93, 38, 47, 70, 1292, 91, 16, 22, 117, 187
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072657. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072658, A072660.

A072636 Permutation of natural numbers induced by reranking plane binary trees given in the standard lexicographic order (A014486) with an "arithmetic global ranking algorithm", using packA054238tr as the packing bijection N X N -> N.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 4, 9, 11, 18, 21, 17, 66, 70, 7, 8, 10, 35, 41, 12, 33, 131, 139, 261, 274, 258, 4101, 4117, 22, 65, 69, 1030, 1090, 81, 1026, 16390, 16454, 20, 23, 19, 68, 72, 13, 14, 36, 521, 547, 42, 515, 8201, 8233, 15, 16, 34, 43, 129, 132, 137, 2059, 2179
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072637. Cf. also A014486, A000695, A054238, A071651, A072634, A072646, A072656, A072658, A072644.

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

Views

Author

Antti Karttunen, Jun 02 2002

Keywords

Links

Crossrefs

Inverse permutation: A072659. Cf. also A014486, A000695, A054238, A048680, A071651, A072634, A072636, A072646, A072656, A072660.
Showing 1-6 of 6 results.

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