A251721 Square array of permutations: A(row,col) = A249822(row, A249821(row+1, col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 2, 1, 3, 2, 1, 5, 3, 2, 1, 4, 4, 3, 2, 1, 7, 6, 4, 3, 2, 1, 11, 7, 5, 4, 3, 2, 1, 6, 9, 6, 5, 4, 3, 2, 1, 13, 10, 7, 6, 5, 4, 3, 2, 1, 17, 5, 8, 7, 6, 5, 4, 3, 2, 1, 10, 12, 10, 8, 7, 6, 5, 4, 3, 2, 1, 19, 15, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 13, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 8, 16, 14, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 19, 15, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset

1,2

Comments

These are the "first differences" between permutations of array A249821, in a sense that by composing the first k rows of this array [from left to right, as in a(n) = row_1(row_2(...(row_k(n))))], one obtains row k+1 of A249821.

On row n, the first A250473(n) terms are fixed, and the first non-fixed term comes at A250474(n).

Links

Table of n, a(n) for n=1..120.

Formula

A(row,col) = A249822(row, A249821(row+1, col)).

A(row,col) = A078898(A246278(row, A246277(A083221(row+1, col)))).

Example

The top left corner of the array:
1, 2, 3, 5, 4, 7, 11, 6, 13, 17, 10, 19, 9, 8, 23, 29, 14, 15, 31, 22, ...
1, 2, 3, 4, 6, 7, 9, 10, 5, 12, 15, 8, 16, 19, 21, 22, 13, 24, 11, 27, ...
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 9, 16, 18, 20, 21, 23, 24, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, ...
...

Prog

(Scheme)
(define (A251721bi row col) (A249822bi row (A249821bi (+ row 1) col)))
(define (A251721 n) (A251721bi (A002260 n) (A004736 n)))
;; Code for A249821bi and A249822bi given in A249821, A249822.

Crossrefs

Inverse permutations can be found from array A251722.

Row 1: A064216, Row 2: A249745, Row 3: A250475.

Cf. A000027, A002260, A004736, A078898, A083221, A246277, A246278, A249821, A249822, A250473, A250474.

Sequence in context: A370628 A207375 A173302 * A251722 A304100 A179314

Adjacent sequences: A251718 A251719 A251720 * A251722 A251723 A251724

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 07 2014

Status

approved