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%I #18 Apr 01 2017 20:52:37
%S 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,
%T 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,
%U 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
%N 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), ...
%C 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.
%C 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.
%F A(row,col) = A249822(row+1, A249821(row, col)).
%F A(row,col) = A078898(A246278(row+1, A246277(A083221(row, col)))).
%e The top left corner of the array:
%e 1, 2, 3, 5, 4, 8, 6, 14, 13, 11, 7, 23, 9, 17, 18, 41, 10, 38, 12, 32, ...
%e 1, 2, 3, 4, 9, 5, 6, 12, 7, 8, 19, 10, 17, 42, 11, 13, 22, 26, 14, 29, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, 14, 9, 10, 21, 11, 12, 13, 15, 33, 16, 25, 17, ...
%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 28, 14, 15, 16, 17, 18, 19, ...
%e ...
%o (Scheme)
%o (define (A251722bi row col) (A249822bi (+ row 1) (A249821bi row col)))
%o (define (A251722 n) (A251722bi (A002260 n) (A004736 n)))
%o ;; Code for A249821bi and A249822bi given in A249821, A249822.
%Y Inverse permutations can be found from array A251721.
%Y Row 1: A048673, Row 2: A249746, Row 3: A250476.
%Y Cf. A000027, A002260, A004736, A078898, A083221, A246277, A246278, A249821, A249822, A250473, A250474.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Dec 07 2014
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