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

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

0,6

References

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

Links

Table of n, a(n) for n=0..92.

Example

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;
  ...

Crossrefs

The rows appear to be converging to A000712.

Row sums are A061552.

Cf. A188919.

Sequence in context: A034853 A242093 A350910 * A244006 A110283 A226290

Adjacent sequences: A322055 A322056 A322057 * A322059 A322060 A322061

Keyword

nonn,tabf

Author

N. J. A. Sloane, Dec 25 2018

Extensions

More terms from Alois P. Heinz, Dec 27 2018

Status

approved