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).
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
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).
A209626
Meandric numbers for a river crossing up to 11 parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28177, 76537, 240343, 665073, 2122968, 5963685, 19295541, 54883588, 179608831, 516272903, 1706070421, 4948280698, 16490889347, 48203859456, 161842379157, 476304741819, 1609703418480, 4765887074059, 16201200791291
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).
A209657
Meandric numbers for a river crossing up to 13 parallel roads at n points.
Original entry on oeis.org
1, 1, 2, 4, 10, 23, 63, 155, 448, 1152, 3452, 9158, 28178, 76539, 240369, 665127, 2123408, 5964627, 19301713, 54897139, 179687084, 516448412, 1707004865, 4950415081, 16501638058, 48228801029, 161963084065, 476588705579, 1611037922998, 4769064680579, 16215807145689
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).
A209660
Meandric numbers for a river crossing up to 14 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, 665128, 2123437, 5964658, 19302248, 54897742, 179695133, 516457890, 1707112980, 4950547189, 16502992754, 48230509790, 161979310981, 476609746441, 1611226513378, 4769315213007, 16217954185533
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).
A209707
Meandric numbers for a river crossing up to 15 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, 2123438, 5964689, 19302281, 54898345, 179695808, 516467363, 1707124038, 4950679082, 16503152306, 48232213024, 161981435856, 476630676669, 1611253336964, 4769563838975, 16218280461398
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).
A210344
Meandric numbers for a river crossing up to 16 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, 5964690, 19302314, 54898380, 179696483, 516468114, 1707135091, 4950691884, 16503311633, 48232404028, 161983554724, 476633293902, 1611280036392, 4769597694865, 16218604538134
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).
A210478
Meandric numbers for a river crossing up to 17 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, 19302315, 54898415, 179696520, 516468865, 1707135922, 4950704681, 16503326351, 48232594797, 161983781556, 476635904628, 1611283232139, 4769631412013, 16218646880868
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 12 results.
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