A293961
Number T(n,k) of linear chord diagrams having n chords and maximal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
Original entry on oeis.org
1, 0, 1, 0, 1, 2, 0, 1, 4, 10, 0, 1, 10, 24, 70, 0, 1, 20, 82, 212, 630, 0, 1, 42, 300, 798, 2324, 6930, 0, 1, 84, 894, 3800, 10078, 30188, 90090, 0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350, 0, 1, 340, 8594, 71624, 313006, 851692, 2545390, 7695828, 22972950
Offset: 0
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 2;
0, 1, 4, 10;
0, 1, 10, 24, 70;
0, 1, 20, 82, 212, 630;
0, 1, 42, 300, 798, 2324, 6930;
0, 1, 84, 894, 3800, 10078, 30188, 90090;
0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350;
...
A293995
Number of linear chord diagrams having n chords and no chord length larger than three.
Original entry on oeis.org
1, 1, 3, 15, 35, 103, 343, 979, 2915, 8935, 26559, 79499, 239547, 717455, 2151095, 6459027, 19371507, 58106071, 174349295, 523022555, 1569013931, 4707208351, 14121515303, 42364215075, 127093528675, 381280144743, 1143838446943, 3431519977579, 10294558387995
Offset: 0
-
LinearRecurrence[{2,1,8,-6},{1,1,3,15},30] (* Harvey P. Dale, Aug 08 2021 *)
A293996
Number of linear chord diagrams having n chords and no chord length larger than four.
Original entry on oeis.org
1, 1, 3, 15, 105, 315, 1141, 4779, 21101, 80559, 314185, 1267551, 5160933, 20504123, 81554685, 326682775, 1310978305, 5239019143, 20931551661, 83743554723, 335175239813, 1340542340399, 5360923216953, 21444223178271, 85786427569333, 343141430067947
Offset: 0
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,2,11,60,-18,-26,-108,-48)
A293997
Number of linear chord diagrams having n chords and no chord length larger than five.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 3465, 14857, 72905, 393565, 2152693, 10317169, 49808117, 247455873, 1256019673, 6371895677, 31696702545, 157383838325, 785587613797, 3938599251649, 19742522444733, 98655068282297, 492637126850897, 2462204077446773, 12316715419452585
Offset: 0
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3, 4, 2, 81, 495, -648, -1590, 208, -5670, -924, 14576, -1536, -2136, -9936, 10656, -2880)
-
CoefficientList[Series[-(24x^11-84x^10+76x^9+20x^8-10x^7-90x^6+12x^5+35x^4+4x^2+2x-1)/((5x-1)(576x^15-2016x^14+1584x^13+744x^12+ 456x^11- 2824x^10-380x^9+ 1058x^8+ 170x^7+352x^6+200x^5-59x^4-28x^3-6x^2-2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[ {3,4,2,81,495,-648,-1590,208,-5670,-924,14576,-1536,-2136,-9936,10656,-2880},{1,1,3,15,105,945,3465,14857,72905,393565,2152693,10317169,49808117,247455873,1256019673,6371895677},30] (* Harvey P. Dale, Jan 03 2024 *)
A293998
Number of linear chord diagrams having n chords and no chord length larger than six.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 10395, 45045, 222951, 1245257, 7689707, 50548041, 328681355, 1898148921, 10938090235, 64447508901, 388656309623, 2372510073525, 14406809496311, 86092382481933, 512757617989667, 3064484085534721, 18400499270245971, 110741448251269561
Offset: 0
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3, 7, 7, 84, 939, 6095, -4433, -31187, -37164, -140858, -899154, -569580, 741066, 3256828, -1225088, 19146692, -26901488, 28568896, 21503648, -89813600, 175998288, -128442288, 44156064, -18953856, 34648704, 69766272, -7008768, 5868288, -82363392, -80815104, -46448640, -9953280)
A293999
Number of linear chord diagrams having n chords and no chord length larger than seven.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 10395, 135135, 675675, 3790647, 23694083, 162961399, 1209395171, 9332799283, 70178707279, 474578729935, 3181796735723, 21683288205723, 150990425051331, 1069361164106091, 7617764489275535, 53863160510249543, 375786310609620379
Offset: 0
A294000
Number of linear chord diagrams having n chords and no chord length larger than eight.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 11486475, 72025173, 497809599, 3759823201, 30676852011, 265149012989, 2341915514787, 19966886272757, 154807536575931, 1184739742163293, 9169888620679203, 72323378114077925, 580752883543676927, 4717664674505952353
Offset: 0
A294001
Number of linear chord diagrams having n chords and no chord length larger than nine.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 218243025, 1512548793, 11451456921, 94099903993, 832822929881, 7850100744697, 77247769844585, 766602148661941, 7301487795390325, 63860693057569633, 549669975975395633, 4765146317902742829
Offset: 0
A294002
Number of linear chord diagrams having n chords and no chord length larger than ten.
Original entry on oeis.org
1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075, 4583103525, 34788783519, 286302699633, 2541730502259, 24202811629589, 245427373661087, 2620070906538825, 28854865779691475, 317259847008270825, 3336850194636528659, 32503486859882091945
Offset: 0
Showing 1-9 of 9 results.
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