A326762 -id:A326762 - cp's OEIS frontend

A326760 Number of permutations of length n whose powers all avoid the pattern 321.

Original entry on oeis.org

1, 2, 5, 12, 28, 70, 161, 386, 932, 2226, 5254, 12748, 30228, 72192

Offset: 1

Amanda Burcroff, Jul 23 2019

Amanda Burcroff and Colin Defant, Pattern-Avoiding Permutation Powers, arXiv:1907.09451 [math.CO], 2019.

Cf. A326761, A326762, A326763.

A326761 Number of 321-avoiding permutations of length n whose squares also avoid the pattern 321.

Original entry on oeis.org

1, 2, 5, 12, 28, 70, 171, 428, 1062, 2664, 6664, 16744, 42018

Offset: 1

Amanda Burcroff, Jul 23 2019

Miklos Bona and Rebecca Smith, Pattern Avoidance in Permutations and Their Squares, arXiv:1901.00026 [math.CO], 2019.
Amanda Burcroff and Colin Defant, Pattern-Avoiding Permutation Powers, arXiv:1907.09451 [math.CO], 2019.

Cf. A326760, A326762, A326763.

A326763 Number of permutations of length n and order at most 3 whose powers all avoid the pattern 132.

Original entry on oeis.org

1, 1, 2, 5, 10, 16, 36, 65, 118, 232, 452, 800, 1622, 3042, 5758, 11077, 21712, 40204, 79718, 151628, 292994, 561954, 1103786, 2087696, 4115506, 7884446, 15393710, 29592074, 58229334, 111422134, 219575234, 422888473, 830617400, 1602832900, 3160618558, 6092881976

Offset: 0

Amanda Burcroff, Aug 15 2019

nonn

Miklós Bóna and Rebecca Smith, Pattern Avoidance in Permutations and Their Squares, Discrete Mathematics, 342 (2019), pp. 3194-3200; arXiv:1901.00026 [math.CO], 2019.
Amanda Burcroff and Colin Defant, Pattern-Avoiding Permutation Powers, Discrete Mathematics, 343 (2020), 112017; arXiv:1907.09451 [math.CO], 2019.

Cf. A326760, A326761, A326762, A001405, A014495, A370686.

def a(n):
    return len([p for p in Permutations(n)
        if p*p == Permutations(n).identity() and p.avoids([1, 3, 2])
        or p*p*p == Permutations(n).identity() and p.avoids([1, 3, 2]) and (p*p).avoids([1, 3, 2])]) # Andrey Zabolotskiy, Apr 13 2025

a(n) = A014495(n) + A370686(n), where the 1st (resp. 2nd) term counts 132-avoiding permutations of order 2 (resp. 1 or 3). - Andrey Zabolotskiy, Apr 13 2025

Terms a(16) onwards using the formula from Andrey Zabolotskiy, Apr 14 2025

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A326760 Number of permutations of length n whose powers all avoid the pattern 321.

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A326761 Number of 321-avoiding permutations of length n whose squares also avoid the pattern 321.

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A326763 Number of permutations of length n and order at most 3 whose powers all avoid the pattern 132.

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