A076876
Meandric numbers for a river crossing two parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 3, 8, 14, 43, 81, 272, 538, 1920, 3926, 14649, 30694, 118489, 252939, 1002994, 2172830, 8805410, 19304190, 79648888, 176343390, 738665040, 1649008456, 6996865599, 15730575554, 67491558466, 152663683494, 661370687363, 1503962954930, 6571177867129
Offset: 0
Let b(n) = A005316(n). Then a(0) = b(0), a(1) = b(1), a(2) = b(1) + b(2), a(3) = b(3) + b(2), a(4) = b(4) + 2*b(3) + 1, a(5) = b(5) + b(3)*b(2) + b(4) + 1.
Consider n=5: if we do not cross the second road there are b(5) = 8 solutions. If we cross the first road 3 times and then the second road twice there are b(3)*b(2) = 2 solutions. If we cross the first road once and the second road 4 times there are b(4) = 3 solutions. The only other possibility is to cross road 1, road 2 twice, road 1 twice and exit to the right.
For larger n it is convenient to give the vector of the number of times the same road is crossed. For example for n=6 the vectors and the numbers of possibilities are as follows:
[6] ...... 14
[5 1] ..... 8
[3 3] ..... 4
[3 2 1] ... 2
[1 5] ..... 8
[1 4 1] ... 3
[1 2 3] ... 2
[1 2 2 1] . 2
Total .... 43
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
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).
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
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).
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
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).
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
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).
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
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).
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
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).
A209383
Meandric numbers for a river crossing up to 8 parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 4, 10, 23, 63, 155, 448, 1151, 3450, 9137, 28134, 76236, 239712, 661374, 2115046, 5921549, 19203568, 54422726, 178585838, 511343777, 1694965469, 4896195579, 16371992897, 47656781437, 160578870274, 470571482142, 1596323368095, 4705798878362, 16059653893209
Offset: 0
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).
A209621
Meandric numbers for a river crossing up to 9 parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3451, 9156, 28155, 76491, 240015, 664363, 2118804, 5954414, 19246816, 54772539, 179063855, 515006165, 1700131496, 4934242781, 16427135058, 48050970367, 161163698861, 474656662565, 1602509174036, 4748224219223, 16125057102402
Offset: 0
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).
A209622
Meandric numbers for a river crossing up to 10 parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9157, 28176, 76514, 240318, 664718, 2122557, 5959052, 19289899, 54828151, 179538447, 515641437, 1705240090, 4941294887, 16481424379, 48127922888, 161736798007, 475487875843, 1608541737898, 4757151493126, 16188528696215
Offset: 0
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).
Showing 1-10 of 19 results.
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