A061552 -id:A061552 - cp's OEIS frontend

A284718 Number of indecomposable permutations avoiding the pattern 1324.

1, 1, 1, 3, 13, 69, 396, 2355, 14363, 89706, 573828, 3758866, 25195016, 172591294, 1206482317, 8592827996, 62257890162, 458214977642, 3421294482237, 25884913987768, 198236423171483, 1535315006313002, 12015208271571543, 94943908405295171, 757044806198966152

Offset: 0

N. J. A. Sloane, Apr 02 2017

nonn

Bjarki Ágúst Guðmundsson, Table of n, a(n) for n = 0..50 (terms 25..50 by Bjarki Ágúst Guðmundsson, computed using Kotesovec's formula and terms from the Conway/Guttmann/Zinn-Justin reference)
Andrew R. Conway, Anthony J. Guttmann and Paul Zinn-Justin, 1324-avoiding permutations revisited, arXiv preprint arXiv:1709.01248 [math.CO], 2017.
A. L. L. Gao, S. Kitaev, P. B. Zhang. On pattern avoiding indecomposable permutations, arXiv:1605.05490 [math.CO], 2016.

Cf. A061552.

For n>1, a(n) = A061552(n) + 3*A000108(n) - A000108(n+1) - 2*A000108(n-1). - Vaclav Kotesovec, Apr 02 2017

More terms from Vaclav Kotesovec, Apr 02 2017

a(0) prepended by Bjarki Ágúst Guðmundsson, Dec 18 2017

A239300 Words of length n over the alphabet {0,...,n-1} that are 1324-avoiding.

Original entry on oeis.org

1, 1, 4, 27, 255, 3028, 41979, 647826, 10807287, 191374095, 3554481788

Offset: 0

Chad Brewbaker, Mar 14 2014

The permutation analog is A061552.

Cf. A000312.

a(8)-a(10) from Giovanni Resta, Mar 14 2014

A322058 Irregular triangle read by rows: T(n,k) = number of 1324-avoiding permutations of length n >= 0 having k >= 0 inversions.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 5, 6, 5, 3, 1, 1, 2, 5, 10, 16, 20, 20, 15, 9, 4, 1, 1, 2, 5, 10, 20, 32, 51, 67, 79, 80, 68, 49, 29, 14, 5, 1, 1, 2, 5, 10, 20, 36, 61, 96, 148, 208, 268, 321, 351, 347, 308, 241, 165, 98, 49, 20, 6, 1, 1, 2, 5, 10, 20, 36, 65, 106, 171, 262, 397, 568, 784, 1019, 1264, 1478, 1628, 1681, 1619, 1441, 1173, 866, 574, 338, 174, 76, 27, 7, 1

Offset: 0

N. J. A. Sloane, Dec 25 2018

			Triangle begins:
  1;
  1;
  1, 1;
  1, 2, 2,  1;
  1, 2, 5,  6,  5,  3,  1;
  1, 2, 5, 10, 16, 20, 20, 15,  9,  4,  1;
  1, 2, 5, 10, 20, 32, 51, 67, 79, 80, 68, 49, 29, 14, 5, 1;
  ...

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 769, Fig. 12.13.

The rows appear to be converging to A000712.
Row sums are A061552.
Cf. A188919.

More terms from Alois P. Heinz, Dec 27 2018

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A284718 Number of indecomposable permutations avoiding the pattern 1324.

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A239300 Words of length n over the alphabet {0,...,n-1} that are 1324-avoiding.

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A322058 Irregular triangle read by rows: T(n,k) = number of 1324-avoiding permutations of length n >= 0 having k >= 0 inversions.

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