

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
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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 ORoperation (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

(Schemefunctions 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



