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A082858 Array A(x,y): the greatest common subtree (intersect) 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). 5
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 1, 1, 3, 2, 2, 3, 1, 1, 0, 0, 1, 1, 3, 2, 5, 2, 3, 1, 1, 0, 0, 1, 2, 3, 1, 2, 2, 1, 3, 2, 1, 0, 0, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 4, 1, 3, 3, 1, 4, 1, 2, 1, 0, 0, 1, 2, 1, 4, 2, 3, 7, 3, 2, 4, 1, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
COMMENTS
Note that together with A082860 this forms a distributive lattice, thus it is possible to compute this function also with the binary AND-operation (A004198) with the help of appropriate mapping functions. I.e. we have A(x,y) = A082857(A004198(A082856(x), A082856(y))).
LINKS
Antti Karttunen, Alternative Catalan Orderings (with the complete Scheme source)
PROG
(Scheme-functions showing the essential idea. For the full source, follow the "Alternative Catalan Orderings" link.)
(define (A082858 n) (A080300 (parenthesization->binexp (GCSB (binexp->parenthesization (A014486 (A025581 n))) (binexp->parenthesization (A014486 (A002262 n)))))))
(define (GCSB t1 t2) (cond ((or (not (pair? t1)) (not (pair? t2))) (list)) (else (cons (GCSB (car t1) (car t2)) (GCSB (cdr t1) (cdr t2))))))
(define (A082858v2 n) (A082857 (A004198bi (A082856 (A025581 n)) (A082856 (A002262 n)))))
CROSSREFS
Cf. A072764. The lower/upper triangular region: A082859. Cf. A080300, A025581, A002262.
Sequence in context: A060953 A339367 A348040 * A363164 A255318 A249223
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 06 2003
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)