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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

Table of n, a(n) for n=1..66.

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.)