A263271 Square array A(row,col): 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).

0, 2, 1, 6, 4, 2, 12, 8, 6, 3, 18, 0, 12, 5, 4, 22, 0, 18, 7, 8, 5, 30, 0, 22, 0, 0, 7, 6, 34, 0, 30, 0, 0, 0, 12, 7, 42, 0, 34, 0, 0, 0, 18, 0, 8, 46, 0, 42, 0, 0, 0, 22, 0, 0, 9, 54, 0, 46, 0, 0, 0, 30, 0, 0, 11, 10, 58, 0, 54, 0, 0, 0, 34, 0, 0, 16, 14, 11

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 (A263271 n) (A263271bi (A002262 n) (A025581 n)))
(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

Column 0: A001477, Column 1: A262686.

Cf. A264971 (number of significant terms on each row, position where the first trailing zero-term occurs).

Cf. A264970.

Cf. also A000005, A045765, A263267.

See also array A265751 constructed in the same way, but obtained by following always the smallest child A082284, instead of the largest child A262686.

Sequence in context: A141715 A329431 A328923 * A098697 A193094 A021466

Adjacent sequences: A263268 A263269 A263270 * A263272 A263273 A263274

Keyword

nonn,tabl

Author

Antti Karttunen, Nov 29 2015

Status

approved