A072764 Tabular N X N -> N bijection induced by Lisp/Scheme function 'cons' combining the two planar binary trees/general trees/parenthesizations encoded by A014486(X) and A014486(Y).

0, 1, 3, 2, 7, 6, 4, 8, 16, 14, 5, 17, 19, 42, 15, 9, 18, 44, 51, 43, 37, 10, 20, 47, 126, 52, 121, 38, 11, 21, 53, 135, 127, 149, 122, 39, 12, 22, 56, 154, 136, 385, 150, 123, 40, 13, 45, 60, 163, 155, 413, 386, 151, 124, 41, 23, 46, 128, 177, 164, 475, 414, 387, 152

Offset

0,3

Links

Table of n, a(n) for n=0..63.

Index entries for the sequences induced by list functions of Lisp

Index entries for sequences that are permutations of the natural numbers

A. Karttunen, Gatomorphisms (with the complete Scheme source)

Prog

(Scheme functions showing the general idea:)
(define (A072764bi x y) (A080300 (parenthesization->binexp (cons (binexp->parenthesization (A014486 x)) (binexp->parenthesization (A014486 y))))))
(define (A072764 n) (cond ((zero? n) n) (else (A072764bi (A025581 (-1+ n)) (A002262 (-1+ n))))))

Crossrefs

Inverse permutation: A072765. a(n) = A069770(A072766(n)). Also transpose of A072766, i.e. a(n) = A072766(A038722(n)). The upper triangular region: A072773. Projection functions are A072771 ('car') & A072772 ('cdr'). The sizes of the corresponding Catalan structures: A072768. The first row: A057548, the first column: A072795, diagonal: A083938. Cf. also A080300, A025581, A002262.

Sequence in context: A268934 A268832 A201566 * A364832 A349890 A130328

Adjacent sequences: A072761 A072762 A072763 * A072765 A072766 A072767

Keyword

nonn,tabl

Author

Antti Karttunen Jun 12 2002

Extensions

a(0)=0 prepended by Sean A. Irvine, Oct 25 2024

Status

approved