A076875 -id:A076875 - cp's OEIS frontend

A210478 Meandric numbers for a river crossing up to 17 parallel roads at n points.

1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28178, 76539, 240370, 665129, 2123439, 5964691, 19302315, 54898415, 179696520, 516468865, 1707135922, 4950704681, 16503326351, 48232594797, 161983781556, 476635904628, 1611283232139, 4769631412013, 16218646880868

Offset: 0

Robert Price, May 07 2012

nonn

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 17 parallel East-West roads n times.

Sequence derived from list of solutions described in A206432.

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column k=17 of A380367.
Cf. A005316 (sequence for one road; extensive references and links).
Cf. A076876 (sequence for two parallel roads).
Cf. A204352, A208062, A208126, A208452, A208453, A209383, A209621, A209622, A209626, A209656, A209657, A209660, A209707, A210344, A210478, A210567, A210592 (sequences for 3 to 19 parallel roads).
Cf. A206432 (sequence for unlimited number of parallel roads).
Cf. A076875, A076906, A076907.

a(21) onwards from Andrew Howroyd, Jan 31 2025

A210567 Meandric numbers for a river crossing up to 18 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28178, 76539, 240370, 665129, 2123439, 5964691, 19302316, 54898416, 179696557, 516468904, 1707136753, 4950705596, 16503341064, 48232611611, 161984008143, 476636172048, 1611286420859, 4769635283158, 16218689069176

Offset: 0

Robert Price, May 07 2012

nonn

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 18 parallel East-West roads n times.

Sequence derived from list of solutions described in A206432.

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column k=18 of A380367.
Cf. A005316 (sequence for one road; extensive references and links).
Cf. A076876 (sequence for two parallel roads).
Cf. A204352, A208062, A208126, A208452, A208453, A209383, A209621, A209622, A209626, A209656, A209657, A209660, A209707, A210344, A210478, A210567, A210592 (sequences for 3 to 19 parallel roads).
Cf. A206432 (sequence for unlimited number of parallel roads).
Cf. A076875, A076906, A076907.

a(21) onwards from Andrew Howroyd, Jan 31 2025

A210592 Meandric numbers for a river crossing up to 19 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28178, 76539, 240370, 665129, 2123439, 5964691, 19302316, 54898417, 179696558, 516468943, 1707136794, 4950706511, 16503342067, 48232628420, 161984027241, 476636439213, 1611286734027, 4769639146736, 16218693724179

Offset: 0

Robert Price, May 07 2012

nonn

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 19 parallel East-West roads n times.

Sequence derived from list of solutions described in A206432.

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column k=19 of A380367.
Cf. A005316 (sequence for one road; extensive references and links).
Cf. A076876 (sequence for two parallel roads).
Cf. A204352, A208062, A208126, A208452, A208453, A209383, A209621, A209622, A209626, A209656, A209657, A209660, A209707, A210344, A210478, A210567, A210592 (sequences for 3 to 19 parallel roads).
Cf. A206432 (sequence for unlimited number of parallel roads).
Cf. A076875, A076906, A076907.

a(21) onwards from Andrew Howroyd, Jan 31 2025

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

Original entry on oeis.org

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

Andrew Howroyd, Jan 31 2025

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

			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 ...
  ...

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

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).

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

cp's OEIS Frontend

A210478 Meandric numbers for a river crossing up to 17 parallel roads at n points.

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A210567 Meandric numbers for a river crossing up to 18 parallel roads at n points.

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A210592 Meandric numbers for a river crossing up to 19 parallel roads at n points.

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

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Author

Keywords

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Examples

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Crossrefs

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