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 A341439 Table of generalized ménage numbers read by antidiagonals upward: T(n,k) is the number of permutations pi in S_k such that pi(i) != i, i+n (mod k) for all i; n, k >= 1. 0
 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 2, 4, 13, 0, 0, 1, 2, 13, 80, 0, 1, 1, 9, 13, 82, 579, 0, 0, 2, 2, 13, 80, 579, 4738, 0, 1, 1, 4, 44, 82, 579, 4740, 43387, 0, 0, 1, 2, 13, 80, 579, 4738, 43387, 439792, 0, 1, 2, 9, 13, 265, 579, 4752, 43390, 439794, 4890741 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS The recurrence for the second row comes from Doron Zeilberger's MENAGE program, available via the arXiv reference. LINKS D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014. FORMULA T(n,n) = A000166(n) for n >= 1. T(1,k) = A000179(k). T(k-1,k) = A000179(k) for k >= 2. T(n,k) = T(n+k, k). T(2,k) = k*T(2,k-1) + 3*T(2,k-2) + (-2*k+6)*T(2,k-3) - 3*T(2,k-4) + (k-6)*T(2,k-5) + T(2,k-6) for k > 8. EXAMPLE Table begins: n\k | 1 2 3 4  5   6    7     8 ----+--------------------------   1 | 0 0 1 2 13  80  579  4738   2 | 0 1 1 4 13  82  579  4740   3 | 0 0 2 2 13  80  579  4738   4 | 0 1 1 9 13  82  579  4752   5 | 0 0 1 2 44  80  579  4738   6 | 0 1 2 4 13 265  579  4740   7 | 0 0 1 2 13  80 1854  4738   8 | 0 1 1 9 13  82  579 14833 CROSSREFS Sequence in context: A071502 A074704 A025247 * A127767 A292577 A055509 Adjacent sequences:  A341436 A341437 A341438 * A341440 A341441 A341442 KEYWORD nonn,tabl AUTHOR Peter Kagey, Feb 11 2021 STATUS approved

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Last modified June 16 13:44 EDT 2021. Contains 345057 sequences. (Running on oeis4.)