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A251722
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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), ...
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13
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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, ...
...
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PROG
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(Scheme)
(define (A251722bi row col) (A249822bi (+ row 1) (A249821bi row col)))
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CROSSREFS
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Inverse permutations can be found from array A251721.
Cf. A000027, A002260, A004736, A078898, A083221, A246277, A246278, A249821, A249822, A250473, A250474.
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KEYWORD
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AUTHOR
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STATUS
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approved
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