OFFSET
0,2
COMMENTS
The square array A(row>=0, col>=0) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...
Each row n lists all the nodes in A263267-tree that one encounters when one starts from node n and always chooses the largest possible child of it (A262686), and then the largest possible child of that child, etc, until a leaf-child (one of the terms of A045765) is encountered, after which the rest of the row contains only zeros.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 antidiagonals
FORMULA
A(row,0) = row and for col >= 1, if A262686(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A262686(row),col-1).
A(0,0) = 0, A(0,1) = 2; if col = 0, A(row,0) = row; and for col > 0, if A(row,col-1) = 0, then A(row,col) = 0, otherwise A(row,col) = A262686(A(row,col-1)). [Another, perhaps more intuitive recurrence for this array.] - Antti Karttunen, Dec 21 2015
EXAMPLE
The top left corner of the array:
0, 2, 6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66, 0, 0, 0, 0
1, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
2, 6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66, 0, 0, 0, 0, 0
3, 5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66, 0, 0, 0, 0, 0, 0
7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
9, 11, 16, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
10, 14, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
11, 16, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
12, 18, 22, 30, 34, 42, 46, 54, 58, 66, 0, 0, 0, 0, 0, 0, 0
13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
14, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
15, 17, 21, 23, 27, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
...
PROG
(Scheme)
(define (A263271bi row col) (cond ((zero? col) row) ((A262686 row) => (lambda (lad) (if (zero? lad) lad (A263271bi lad (- col 1)))))))
;; An alternative implementation, reflecting the new recurrence:
(define (A263271bi row col) (cond ((zero? col) row) ((and (zero? row) (= 1 col)) 2) ((zero? (A263271bi row (- col 1))) 0) (else (A262686 (A263271bi row (- col 1))))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Nov 29 2015
STATUS
approved