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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). 4
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 (list; table; graph; refs; listen; history; text; internal format)
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.

A. 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: A231205 A003984 A087061 * A283845 A058071 A174961

Adjacent sequences:  A082857 A082858 A082859 * A082861 A082862 A082863

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen May 06 2003

STATUS

approved

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Last modified August 21 05:48 EDT 2019. Contains 326162 sequences. (Running on oeis4.)