A324428
Number T(n,k) of labeled cyclic chord diagrams with n chords such that every chord has length at least k; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
Original entry on oeis.org
1, 3, 1, 15, 4, 1, 105, 31, 7, 1, 945, 293, 68, 11, 1, 10395, 3326, 837, 159, 18, 1, 135135, 44189, 11863, 2488, 381, 29, 1, 2027025, 673471, 189503, 43169, 7601, 879, 47, 1, 34459425, 11588884, 3377341, 822113, 160784, 23559, 2049, 76, 1, 654729075, 222304897, 66564396, 17066007, 3621067, 607897, 72989, 4788, 123, 1
Offset: 1
Triangle T(n,k) begins:
1;
3, 1;
15, 4, 1;
105, 31, 7, 1;
945, 293, 68, 11, 1;
10395, 3326, 837, 159, 18, 1;
135135, 44189, 11863, 2488, 381, 29, 1;
2027025, 673471, 189503, 43169, 7601, 879, 47, 1;
...
-
b:= proc(n, f, m, l, j) option remember; (k-> `if`(n `if`(n=0 or k<2, doublefactorial(2*n-1),
b(2*n-k+1, [1$k-1], 0, [0$k-1], k-1)):
seq(seq(T(n, k), k=1..n), n=1..10);
-
b[n_, f_List, m_, l_List, j_] := b[n, f, m, l, j] = Function[k, If[n < Total[f] + m + Total[l], 0, If[n == 0, 1, Sum[If[f[[i]] == 0, 0, b[n - 1, ReplacePart[f, i -> 0], m + l[[1]], Append[ReplacePart[l, 1 -> Nothing], 0], Max[0, j - 1]]],{i, Max[1, j + 1], Min[k, n - 1]}] + If[m == 0, 0, m*b[n - 1, f, m - 1 + l[[1]], Append[ReplacePart[l, 1 -> Nothing], 0], Max[0, j - 1]]] + b[n - 1, f, m + l[[1]], Append[ReplacePart[l, 1 -> Nothing], 1], Max[0, j - 1]]]]][Length[l]];
T[n_, k_] := If[n == 0 || k < 2, 2^(n-1) Pochhammer[3/2, n-1], b[2n-k+1, Table[1, {k-1}], 0, Table[0, {k-1}], k-1]];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 27 2020, after Alois P. Heinz *)
A324445
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals one.
Original entry on oeis.org
1, 2, 11, 74, 652, 7069, 90946, 1353554, 22870541, 432424178, 9044698456, 207336529399, 5168830168426, 139221843251594, 4028994710377547, 124670425690921634, 4107486007743301396, 143555848444786921189, 5304751937400100397626, 206646474536314180818218
Offset: 1
A324446
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals two.
Original entry on oeis.org
1, 3, 24, 225, 2489, 32326, 483968, 8211543, 155740501, 3265307342, 74995101843, 1872508994356, 50500982610620, 1463062187672336, 45314261742435296, 1494164679669072424, 52257665502536426741, 1932255827699763531474, 75312621088768346098203
Offset: 2
A324447
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals three.
Original entry on oeis.org
1, 6, 57, 678, 9375, 146334, 2555228, 49498389, 1054882116, 24545326598, 619415271672, 16854164945997, 491956017936245, 15335174679459134, 508475723159116576, 17870522292434937714, 663618269365250877446, 25964529622925026990819, 1067602511902741954478695
Offset: 3
A324448
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals four.
Original entry on oeis.org
1, 10, 141, 2107, 35568, 661329, 13444940, 297333278, 7122103435, 183969320652, 5102519835609, 151340386825771, 4782068352314304, 160422533608810186, 5695524314835911655, 213389274860898491690, 8414796730663230017112, 348422910620718837979244
Offset: 4
A324449
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals five.
Original entry on oeis.org
1, 17, 352, 6722, 137225, 3013170, 70909863, 1785795023, 48031299838, 1376860759082, 41968192206641, 1356883954535010, 46416330714749286, 1675869323349039899, 63713356727612022712, 2544933663663025077386, 106578973284507947559875, 4670547639650409700162167
Offset: 5
A324450
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals six.
Original entry on oeis.org
1, 28, 832, 21510, 534908, 13859131, 376302024, 10758388849, 324301515064, 10305945419380, 345043568421088, 12157186490730430, 450167342192163864, 17492055607930262356, 712111923015875566112, 30325363998402690968142, 1348761584058475514807527
Offset: 6
A324451
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals seven.
Original entry on oeis.org
1, 46, 1973, 68201, 2098472, 64097193, 2008704765, 65104369974, 2195744407327, 77260041066718, 2838770935775962, 108941687605845691, 4365240928102864872, 182511493727454453315, 7955490810231969340127, 361168545333805402618994, 17059236243411156603252558
Offset: 7
A324452
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals eight.
Original entry on oeis.org
1, 75, 4665, 210738, 8209677, 297511656, 10758827632, 395523803515, 14915877669600, 580537472007709, 23391018103358991, 977123638431619844, 42348895992865182235, 1904609547261379880531, 88871688665105062492072, 4300641510854505723773724
Offset: 8
A324453
Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals nine.
Original entry on oeis.org
1, 122, 10980, 651962, 31844074, 1382524706, 57759507054, 2408367427106, 101604258942813, 4373090645047650, 193104747980308379, 8776137990134208386, 411230178369151616856, 19887402814123893337150, 993118621992840412774504, 51217036176798656934165346
Offset: 9
Showing 1-10 of 11 results.
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