cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 24 results. Next

A076875 Meandric numbers for a curve crossing two perpendicular lines at n points.

Original entry on oeis.org

1, 2, 4, 10, 22, 62, 176, 436
Offset: 0

Views

Author

N. J. A. Sloane and Jon Wild, Nov 24 2002

Keywords

Comments

a(n) = number of ways that a curve can start in the (-,-) quadrant, cross the x and y axes at exactly n points and end in any quadrant. Line is undirected.

Examples

			See illustration for a(4)=22: each of the 12 solutions shown crosses the x-axis first and ten of them are related by mirror symmetry to a corresponding curve that crosses the y-axis first, making the total a(4)=22.

Links

Crossrefs

Cf. A005316, A076876, A076906, A076907 (directed case).

Formula

For n odd a(n) = 2*A076906(n).

Extensions

a(6) and a(7) corrected Aug 23 2003
a(7) corrected by Robert Price, Jul 29 2012

A076907 Meandric numbers for a river crossing two perpendicular roads at n points, beginning in the (-,-) quadrant and ending in any quadrant.

Original entry on oeis.org

2, 2, 6, 10, 32, 62, 210, 436, 1540, 3346, 12192, 27344, 102054, 234388, 891574, 2085940, 8057844, 19134786, 74864648, 179968564, 711708544
Offset: 0

Views

Author

N. J. A. Sloane and Jon Wild, Nov 26 2002

Keywords

Comments

a(n) = number of ways that a directed curve (or arrow) can start in the (-,-) quadrant, cross the x and y axes at exactly n points and end in any quadrant.

Crossrefs

Cf. A005316, A076876, A076906, A076875 (undirected case).
Cf. A077551 (cross x axis first).

Formula

a(2n+1) = 2*A076906(2n+1).

Extensions

a(6) and a(7) corrected Aug 25 2003
a(7) corrected by Robert Price, Jul 29 2012
a(8)-a(20) from Robert Price, Aug 01 2012

A076906 Meandric numbers for a river (or directed line) crossing two perpendicular roads at n points, beginning in the (-,-) quadrant and ending in the (+,+) quadrant if n even, in the (+,-) quadrant if n odd.

Original entry on oeis.org

0, 1, 2, 5, 12, 31, 82, 218, 612, 1673, 4892, 13672, 41192, 117194, 361302, 1042970, 3274712, 9567393, 30490688, 89984282, 290353456
Offset: 0

Views

Author

N. J. A. Sloane and Jon Wild, Nov 26 2002

Keywords

Crossrefs

Cf. A005316, A076875 (undirected line), A076876, A076907 (end anywhere).

Extensions

a(7) corrected Aug 25 2003
a(7) corrected and a(8)-a(20) added by Robert Price, Jul 29 2012

A209656 Meandric numbers for a river crossing up to 12 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28178, 76538, 240368, 665100, 2123379, 5964156, 19301178, 54890366, 179679030, 516360755, 1706896545, 4949350203, 16500278295, 48216373545, 161946759019, 476447428528, 1610847688579, 4767486352733, 16213635060406
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 12 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

Column k=12 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.

Extensions

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

A204352 Meandric numbers for a river crossing up to 3 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 9, 21, 52, 131, 345, 915, 2519, 6926, 19711, 55674, 162594, 468929, 1398129, 4100003, 12433282, 36960316, 113678461, 341785050, 1063890616, 3229522688, 10156518859, 31085477306, 98635931623, 304048850048, 972323924567, 3015979607106, 9711570455824
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross 3 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

Column k=3 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.

Extensions

a(21)-a(40) from Andrew Howroyd, Dec 07 2015

A206432 Meandric numbers for a river crossing any number of 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, 179696559, 516468945, 1707136837, 4950706599, 16503343162, 48232630706, 161984048816, 476636485050, 1611287098347, 4769639932874, 16218699278307
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross any number of parallel East-West roads n times.
Of course, the number of roads crossed cannot be more than the number of crossings, n.
A file (28GB) listing all solutions through n=20 is available from the author.

Links

Crossrefs

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. A076875, A076906, A076907.

Extensions

a(21)-a(30) from Andrew Howroyd, Dec 07 2015

A208062 Meandric numbers for a river crossing up to 4 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 22, 61, 142, 420, 1017, 3146, 7844, 25083, 63974, 209875, 545060, 1824949, 4810138, 16374993, 43695535, 150820899, 406669871, 1420155120, 3863613980, 13627843933, 37363313071, 132933980698, 366939582498, 1315436809855, 3652777067949, 13182411646150
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 4 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

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.

Extensions

a(21)-a(36) from Andrew Howroyd, Dec 05 2015

A208126 Meandric numbers for a river crossing up to 5 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 62, 153, 433, 1120, 3281, 8776, 26399, 72423, 222496, 622616, 1946044, 5533227, 17545134, 50545069, 162237507, 472541542, 1532707268, 4506042037, 14748997812, 43709690021, 144213436887, 430371626111, 1429980808522, 4293569179189, 14355812667699
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 5 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

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.

Extensions

a(21)-a(36) from Andrew Howroyd, Dec 05 2015

A208452 Meandric numbers for a river crossing up to 6 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 63, 154, 446, 1135, 3416, 8947, 27712, 74204, 235041, 640552, 2065849, 5711840, 18696838, 52321747, 173413647, 490279035, 1642287831, 4684178185, 15834649146, 45511151647, 155077912223, 448722569787, 1539743907074, 4481866870316, 15474663284941
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 6 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

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.

Extensions

a(21)-a(36) from Andrew Howroyd, Dec 05 2015

A208453 Meandric numbers for a river crossing up to 7 parallel roads at n points.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 63, 155, 447, 1150, 3433, 9118, 27923, 75981, 237379, 658380, 2090519, 5888530, 18951534, 54069881, 176020213, 507632647, 1668910009, 4857449082, 16106998656, 47253245257, 157874165288, 466367068388, 1568587476660, 4661900731148, 15773729508730
Offset: 0

Views

Author

Robert Price, May 07 2012

Keywords

Comments

Number of ways that a river (or directed line) that starts in the South and flows East can cross up to 7 parallel East-West roads n times.
Sequence derived from list of solutions described in A206432.

Links

Crossrefs

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.

Extensions

a(21)-a(36) from Andrew Howroyd, Dec 05 2015
Showing 1-10 of 24 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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