A152612
Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.
Original entry on oeis.org
1, 8, 49, 681, 14721, 524137, 25471105, 1628116890, 131789656610, 13174980291658, 1593894406662866, 229496526010111571, 38782290669508033003, 7600987633299112125995, 1710169549495739472301076, 437793904386312274903991653, 126520458075485848061740557461
Offset: 1
- J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
- Álvar Ibeas, Table of n, a(n) for n = 1..60
- Joseph Ben Geloun and Sanjaye Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, Annales de l'Institut Henri Poincaré D, Vol. 1, No. 1 (2014), pp. 77-138; arXiv preprint, arXiv:1307.6490 [hep-th], 2013.
- Jin Ho Kwak and Jaeun Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.
-
A057006 = Import["https://oeis.org/A057006/b057006.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
a = etr[A057006[[#]]&];
Array[a, 15] (* Jean-François Alcover, Aug 29 2019 *)
-
[sum(p.aut()**2 for p in Partitions(n)) for n in range(1,8)] # Álvar Ibeas, Mar 24 2015
a(6) and a(7) from Geloun and Ramgoolan (2013) added by
N. J. A. Sloane, Nov 21 2013
Name clarified and more terms added by
Álvar Ibeas, Mar 24 2015
A057009
Number of conjugacy classes of subgroups of index 3 in free group of rank n.
Original entry on oeis.org
1, 7, 41, 235, 1361, 7987, 47321, 281995, 1685921, 10096867, 60524201, 362972155, 2177309681, 13062280147, 78368930681, 470199300715, 2821152888641, 16926788453827, 101560343826761, 609360901747675, 3656161925798801, 21936961098633907, 131621735219132441
Offset: 1
- R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
- J. H. Kwak and J. Lee, Enumeration of connected graph coverings, J. Graph Th., 23 (1996), 105-109.
- J. H. Kwak and J. Lee, Enumeration of graph coverings and surface branched coverings, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.
- V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.
- Index entries for linear recurrences with constant coefficients, signature (11,-36,36).
-
[6^(n-1)+3^(n-1)-2^(n-1): n in [1..30]] /* or */ I:=[1,7,41]; [n le 3 select I[n] else 11*Self(n-1)-36*Self(n-2)+36*Self(n-3): n in [1..30]]; // Vincenzo Librandi, May 12 2015
-
Table[6^(n-1)+3^(n-1)-2^(n-1),{n,25}] (* or *) LinearRecurrence[ {11,-36,36},{1,7,41},25] (* Harvey P. Dale, Nov 24 2011 *)
CoefficientList[Series[(1 - 4 x)/((1 - 2 x) (1 - 3 x) (1 - 6 x)), {x, 0, 33}], x] (* Vincenzo Librandi, May 12 2015 *)
-
a(n)=if(n<0,0,6^(n-1)+3^(n-1)-2^(n-1))
More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001
A069738
Number of isomorphism classes of minimal n-extensions of a kind of homeomorphism of the circle.
Original entry on oeis.org
1, 3, 7, 26, 97, 624, 4162, 34469
Offset: 1
- N. G. Markley and W. N. Anderson,jun, An application of Moebius inversion to a problem in topological dynamics. Bull. Amer. Math. Soc. 79 (1973), 1027-1029.
- V. A. Liskovets, On a combinatorial problem of the theory of topological transformations of the circle. Vesci AN BSSR (ser. fiz.-mat.), No 4 (1976), 29-34 (in Russian), Math. Rev. 58 #7575.
Showing 1-3 of 3 results.
Comments