A251722 Square array of permutations: A(row,col) = A249822(row+1, A249821(row, 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, 8, 9, 4, 3, 2, 1, 6, 5, 5, 4, 3, 2, 1, 14, 6, 6, 5, 4, 3, 2, 1, 13, 12, 7, 6, 5, 4, 3, 2, 1, 11, 7, 8, 7, 6, 5, 4, 3, 2, 1, 7, 8, 14, 8, 7, 6, 5, 4, 3, 2, 1, 23, 19, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 17, 21, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 42, 11, 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 A249822, in a sense that by composing the first k rows of this array [from right to left, as in a(n) = row_k(...(row_2(row_1(n))))], one obtains row k+1 of A249822.

On row n the first non-fixed term is A250474(n+1) at position A250474(n), i.e., on row 1 it is 5 at n=4, on row 2 it is 9 at n=5, on row 3 it is 14 at n=9, etc. All the previous A250473(n) terms are fixed.

Links

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

Formula

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

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

Example

The top left corner of the array:
1, 2, 3, 5, 4, 8, 6, 14, 13, 11, 7, 23, 9, 17, 18, 41, 10, 38, 12, 32, ...
1, 2, 3, 4, 9, 5, 6, 12, 7, 8, 19, 10, 17, 42, 11, 13, 22, 26, 14, 29, ...
1, 2, 3, 4, 5, 6, 7, 8, 14, 9, 10, 21, 11, 12, 13, 15, 33, 16, 25, 17, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 28, 14, 15, 16, 17, 18, 19, ...
...

Prog

(Scheme)
(define (A251722bi row col) (A249822bi (+ row 1) (A249821bi row col)))
(define (A251722 n) (A251722bi (A002260 n) (A004736 n)))
;; Code for A249821bi and A249822bi given in A249821, A249822.

Crossrefs

Inverse permutations can be found from array A251721.

Row 1: A048673, Row 2: A249746, Row 3: A250476.

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

Sequence in context: A207375 A173302 A251721 * A304100 A179314 A204927

Adjacent sequences: A251719 A251720 A251721 * A251723 A251724 A251725

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 07 2014

Status

approved