Among permutations of length N, how many satisfy |a_i − i| ≠ K

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Among permutations of length N, how many satisfy |a_i − i| ≠ K

Revision en3, by elizabeth_zou_fanboi, 2024-11-08 20:02:58

Among the N! permutations of length N, how many satisfy |a_i − i| ≠ K

Constraints: 2 ≤ N ≤ 2000

1 ≤ K ≤ N − 1

Revisions

Rev.	By	When	Δ	Comment
en7	elizabeth_zou_fanboi	2024-11-09 21:04:04	2783	Reverted to en5
en6	elizabeth_zou_fanboi	2024-11-09 21:03:06	2783	Reverted to en4
en5	elizabeth_zou_fanboi	2024-11-09 21:00:28	2783
en4	elizabeth_zou_fanboi	2024-11-08 20:51:00	112
en3	elizabeth_zou_fanboi	2024-11-08 20:02:58	4	Tiny change: 'N ≤ 2000\n1 ≤ K ≤ ' -> 'N ≤ 2000\n\n\n1 ≤ K ≤ ' (published)
en2	elizabeth_zou_fanboi	2024-11-08 20:02:30	4	Tiny change: '− i\| ≠ K\nConstrai' -> '− i\| ≠ K\n\n\nConstrai' (saved to drafts)
en1	elizabeth_zou_fanboi	2024-11-08 20:02:12	174	Initial revision (published)