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A251721
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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), ...
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13
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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
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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 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).
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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, 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, ...
...
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PROG
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(Scheme)
(define (A251721bi row col) (A249822bi row (A249821bi (+ row 1) col)))
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CROSSREFS
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Inverse permutations can be found from array A251722.
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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