A369589 -id:A369589 - cp's OEIS frontend

A369588 Triangular array read by rows: T(m,n) = number of Yamanouchi words of length m that start with n, m >= 1, n = 1..m.

1, 1, 1, 2, 1, 1, 4, 3, 2, 1, 10, 7, 5, 3, 1, 26, 20, 14, 11, 4, 1, 76, 56, 44, 31, 19, 5, 1, 232, 182, 139, 106, 69, 29, 6, 1, 764, 589, 475, 351, 265, 127, 41, 7, 1, 2620, 2088, 1658, 1303, 971, 583, 209, 55, 8, 1, 9496, 7522, 6146, 4846, 3734, 2446, 1106, 319, 71, 9, 1, 35696, 28820, 23495, 19108, 14629, 10616, 5323, 1904, 461, 89, 10, 1

Offset: 1

Max Alekseyev, Jan 26 2024

			Array starts with
  m=1:  1
  m=2:  1,  1
  m=3:  2,  1,  1
  m=4:  4,  3,  2,  1
  m=5: 10,  7,  5,  3,  1
  m=6: 26, 20, 14, 11,  4, 1
  m=7: 76, 56, 44, 31, 19, 5, 1

Wikipedia, Lattice word.

Sum in the m-th row equals T(m+1,1) = A000085(m).
Columns: A000085 (n=1), A238124 (n=2), A369590 (n=3).
Cf. A369589.

A369591 a(n) = number of Yamanouchi words over the alphabet {1, 2, 3} of length n that start with 3.

Original entry on oeis.org

0, 0, 1, 2, 5, 14, 35, 90, 245, 644, 1716, 4707, 12727, 34683, 96174, 264784, 732785, 2051338, 5719684, 16007081, 45160093, 127106181, 358743903, 1018566177, 2887666445, 8204375034

Offset: 1

Max Alekseyev, Jan 26 2024

Column 3 in A369589.
Number of Yamanouchi words over the alphabet {1, 2, 3} is given by A001006, and by A217323 for the words containing 3.
Cf. A238728, A369590.

cp's OEIS Frontend

A369588 Triangular array read by rows: T(m,n) = number of Yamanouchi words of length m that start with n, m >= 1, n = 1..m.

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A369591 a(n) = number of Yamanouchi words over the alphabet {1, 2, 3} of length n that start with 3.

Views

Author

Keywords

Crossrefs