A380367 Array read by antidiagonals: meandric numbers for a river crossing up to k parallel roads at n points, n >= 0, k >= 1.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 3, 1, 1, 2, 4, 8, 8, 1, 1, 2, 4, 9, 14, 14, 1, 1, 2, 4, 10, 21, 43, 42, 1, 1, 2, 4, 10, 22, 52, 81, 81, 1, 1, 2, 4, 10, 23, 61, 131, 272, 262, 1, 1, 2, 4, 10, 23, 62, 142, 345, 538, 538, 1, 1, 2, 4, 10, 23, 63, 153, 420, 915, 1920, 1828

Offset

0,9

Comments

Illustrations of the initial terms for the case of two parallel roads can be found in A076876.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..945 (first 43 antidiagonals)

Formula

T(n,k) = T(n,n) for k > n.

Example

Array begins:
===================================================
n\k |   1   2   3    4    5    6    7    8    9 ...
----+----------------------------------------------
  0 |   1   1   1    1    1    1    1    1    1 ...
  1 |   1   1   1    1    1    1    1    1    1 ...
  2 |   1   2   2    2    2    2    2    2    2 ...
  3 |   2   3   4    4    4    4    4    4    4 ...
  4 |   3   8   9   10   10   10   10   10   10 ...
  5 |   8  14  21   22   23   23   23   23   23 ...
  6 |  14  43  52   61   62   63   63   63   63 ...
  7 |  42  81 131  142  153  154  155  155  155 ...
  8 |  81 272 345  420  433  446  447  448  448 ...
  9 | 262 538 915 1017 1120 1135 1150 1151 1152 ...
  ...

Crossrefs

Columns 1..19 are A005316, A076876, A204352, A208062, A208126, A208452, A208453, A209383, A209621, A209622, A209626, A209656, A209657, A209660, A209707, A210344, A210478, A210567, A210592.

Main diagonal is A206432.

Cf. A076875 (perpendicular roads).

Sequence in context: A378562 A334046 A136605 * A165621 A284321 A004739

Adjacent sequences: A380364 A380365 A380366 * A380368 A380369 A380370

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 31 2025

Status

approved