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A153250
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Array A(x,y): A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ... formed by growing a bud (a single V-node) to the yth leaf of the binary tree A014486(x).
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3
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1, 0, 2, 0, 3, 4, 0, 0, 5, 6, 0, 0, 6, 7, 9, 0, 0, 0, 8, 10, 11, 0, 0, 0, 0, 11, 12, 14, 0, 0, 0, 0, 14, 13, 15, 16, 0, 0, 0, 0, 0, 15, 16, 17, 19, 0, 0, 0, 0, 0, 0, 19, 18, 20, 23, 0, 0, 0, 0, 0, 0, 0, 20, 21, 24, 25, 0, 0, 0, 0, 0, 0, 0, 0, 22, 25, 26, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 27, 29, 30
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Note: the leaf-positions are indexed so that the rightmost one in the tree is the leaf 0, et cetera, up to the leftmost one, which is the leaf with index A072643(x). In this manner, terms on each row stay in monotone order. Row n (starting from row 0) contains A072643(n)+1 non-zero terms and then infinite number of zeros after that. A153249 gives only the non-zero terms. Can be used to compute "fleeing tree" sequences for Catalan bijections. See comments at A153246.
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..1274
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EXAMPLE
| Top left corner of array:
1, 0, 0, 0, 0, ...
2, 3, 0, 0, 0, ...
4, 5, 6, 0, 0, ...
6, 7, 8, 0, 0, ...
9,10,11,14, 0, ...
11,12,13,15, 0, ...
14,15,16,19, 0, ...
By inserting a bud (\/) to the leaf-position 1 of binary tree A014486(2) (leaf-positions numbered for clarification):
....1....0
.....\../
..2...\/
...\../
....\/
we obtain a binary tree:
.......
.\../..
..\/...
...\../
....\/
.\../
..\/
which is the 5th binary tree encoded by A014486. Thus A(2,1)=5.
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PROG
| (MIT Scheme:)
(define (A153250 n) (A153250bi (A002262 n) (A025581 n)))
(define (A153250bi x y) (A080300 (parenthesization->a014486 (bud! (A014486->parenthesization (A014486 x)) y))))
(define (bud! s i) (replace-nth-leaf! s i (list (list))))
(define (replace-nth-leaf! s i scion) (cond ((> i (count-pars s)) (quote ())) ((null? s) scion) (else (let ((leafs-to-visit i)) (call-with-current-continuation (lambda (exit) (let fork ((s s)) (cond ((null? (cdr s)) (if (zero? leafs-to-visit) (exit (set-cdr! s scion)) (set! leafs-to-visit (-1+ leafs-to-visit)))) (else (fork (cdr s)))) (cond ((null? (car s)) (if (zero? leafs-to-visit) (exit (set-car! s scion)) (set! leafs-to-visit (-1+ leafs-to-visit)))) (else (fork (car s))))))) s))))
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CROSSREFS
| A002262, A025581.
Sequence in context: A112239 A021835 A112476 * A102389 A099091 A078436
Adjacent sequences: A153247 A153248 A153249 * A153251 A153252 A153253
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 22 2008
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