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 A339941 Triangle read by rows: T(n,k) is the number of permutations of {1,...,n} whose longest embedded arithmetic progression has length k. 1
 1, 0, 2, 0, 4, 2, 0, 10, 12, 2, 0, 20, 82, 16, 2, 0, 48, 516, 134, 20, 2, 0, 104, 3232, 1480, 198, 24, 2, 0, 282, 21984, 15702, 2048, 274, 28, 2, 0, 496, 168368, 162368, 28048, 3204, 362, 32, 2, 0, 1066, 1306404, 1902496, 374194, 39420, 4720, 462, 36, 2, 0, 2460, 11064306, 23226786, 4929828, 622140, 64020, 6644, 574, 40, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Asymptotics can be found in Goh and Zhao (2020). The column k=2 corresponds to the number of 3-free permutations of 1..n, for n>=2. LINKS M. K. Goh and R. Y. Zhao, Arithmetic subsequences in a random ordering of an additive set, arXiv:2012.12339 [math.CO], 2020. EXAMPLE Triangle T(n,k) begins:   n/k 1    2         3         4        5       6      7     8    9 10 11 12    1  1    2  0    2    3  0    4         2    4  0   10        12         2    5  0   20        82        16        2    6  0   48       516       134       20       2    7  0  104      3232      1480      198      24      2    8  0  282     21984     15702     2048     274     28     2    9  0  496    168368    162368    28048    3204    362    32    2   10  0 1066   1306404   1902496   374194   39420   4720   462   36   2   11  0 2460  11064306  23226786  4929828  622140  64020  6644  574  40  2   12  0 6128 101355594 298314654 68584052 9719492 913440 98472 9024 698 44 2 CROSSREFS Cf. A003407 (column k=2), A338993, A339942. Sequence in context: A081880 A144289 A293815 * A211318 A324239 A274706 Adjacent sequences:  A339938 A339939 A339940 * A339942 A339943 A339944 KEYWORD nonn,tabl AUTHOR Marcel K. Goh, Dec 23 2020 STATUS approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)