A082860 Array A(x,y): the least common supertree (union) of the binary trees x and y, (x,y) running as (0,0),(1,0),(0,1),(2,0),(1,1),(0,2) and each index referring to a binary tree encoded by A014486(j).

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 2, 3, 4, 5, 4, 6, 6, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 14, 14, 5, 6, 7, 8, 7, 6, 15, 4, 15, 6, 7, 8, 9, 8, 16, 6, 11, 11, 6, 16, 8, 9, 10, 9, 19, 7, 14, 5, 14, 7, 19, 9, 10, 11, 10, 9, 8, 42, 15, 15, 42, 8, 9, 10, 11, 12, 11, 10, 37, 51, 43, 6, 43, 51, 37, 10, 11, 12, 13, 12, 11, 38, 9, 52, 16, 16, 52, 9, 38, 11, 12, 13, 14, 13, 12

Offset

0,4

Comments

Note that together with A082858 this forms a distributive lattice, thus it is possible to compute this function also with the binary OR-operation (A003986) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A003986(A082856(x), A082856(y))).

Links

Table of n, a(n) for n=0..107.

Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)

Index entries for sequences related to lattices

Prog

(Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
(define (A082860 n) (A080300 (parenthesization->binexp (LCSB (binexp->parenthesization (A014486 (A025581 n))) (binexp->parenthesization (A014486 (A002262 n)))))))
(define (LCSB t1 t2) (cond ((and (not (pair? t1)) (not (pair? t2))) (list)) (else (cons (LCSB (car* t1) (car* t2)) (LCSB (cdr* t1) (cdr* t2))))))
(define (car* p) (if (pair? p) (car p) p))
(define (cdr* p) (if (pair? p) (cdr p) p))
(define (A082860v2 n) (A082857 (A003986bi (A082856 (A025581 n)) (A082856 (A002262 n)))))

Crossrefs

The lower/upper triangular region: A082861. Cf. A072764, A080300, A025581, A002262.

Sequence in context: A087061 A344838 A344835 * A342859 A342385 A367108

Adjacent sequences: A082857 A082858 A082859 * A082861 A082862 A082863

Keyword

nonn,tabl

Author

Antti Karttunen, May 06 2003

Status

approved