A079265
Number of antisymmetric transitive binary relations on n unlabeled points.
Original entry on oeis.org
1, 2, 7, 32, 192, 1490, 15067, 198296, 3398105, 75734592, 2191591226, 82178300654, 3984499220967, 249298391641352, 20089200308020179, 2081351202770089728
Offset: 0
- A. Hess and H. Iyer, Enumeration of mixed linear models and SAS macro for computation of confidence intervals for variance components, presented at Applied Statistics in Agriculture Conference at Kansas State University 2001.
- R. Bayon, N. Lygeros and J.-S. Sereni, New progress in enumeration of mixed models, Applied Mathematics E-Notes, 5 (2005), 60-65.
- R. Bayon, N. Lygeros and J.-S. Sereni, Nouveaux progrès dans l'énumération des modèles mixtes, in Knowledge discovery and discrete mathematics : JIM'2003, INRIA, Université de Metz, France, 2003, pp. 243-246.
- Gunnar Brinkmann and Brendan D. McKay, Counting unlabelled topologies and transitive relations.
- Gunnar Brinkmann and Brendan D. McKay, Counting Unlabelled Topologies and Transitive Relations, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.1.
- R. Fraïssé and N. Lygeros, Petits posets: dénombrement, représentabilité par cercles et "compenseurs", C. R. Acad. Sci. Paris, Vol. 313, series I, pp. 417-420, 1991.
- Ann Marie Hess, Mixed Models Site
- G. Pfeiffer, Counting Transitive Relations, preprint, 2004.
- G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
a(10)-a(12) and new description from Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004
a(13)-a(15) from Brinkmann's and McKay's paper by
Vladeta Jovovic, Jan 04 2006
A079263
Number of constrained mixed models with n factors.
Original entry on oeis.org
2, 6, 22, 101, 576, 4162, 38280, 451411, 6847662, 133841440
Offset: 1
- A. Hess and H. Iyer, Enumeration of mixed linear models and SAS macro for computation of confidence intervals for variance components, presented at Applied Statistics in Agriculture Conference at Kansas State University 2001.
- R. Bayon, N. Lygeros and J.-S. Sereni, New progress in enumeration of mixed models, Applied Mathematics E-Notes, 5 (2005), 60-65.
- R. Bayon, N. Lygeros and J.-S. Sereni, Nouveaux progrès dans l'énumération des modèles mixtes, in Knowledge discovery and discrete mathematics : JIM'2003, INRIA, Université de Metz, France, 2003, pp. 243-246.
- R. Fraïssé and N. Lygeros, Petits posets: dénombrement, représentabilité par cercles et "compenseurs", C. R. Acad. Sci. Paris, Vol. 313, series I, pp. 417-420, 1991.
- Ann Marie Hess, Mixed Models Site
a(10) from Bayon, Lygeros, and Sereni (2005) added by
Sean A. Irvine, Aug 05 2025
A353041
G.f. A(x) satisfies: A(x) = 1 + x * A(3*x/(1 + 2*x)) / (1 - x).
Original entry on oeis.org
1, 1, 4, 34, 820, 62140, 14651728, 10547347384, 22950318347248, 150277943334242320, 2955664382713520203072, 174478760893191691170298912, 30905073486465684713191125079360, 16423574117627547687292156418920831936, 26184104208316120602662312616366633316565248
Offset: 0
-
nmax = 14; A[] = 0; Do[A[x] = 1 + x A[3 x/(1 + 2 x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n - 1, k - 1] 3^(k (k - 1)/2), {k, 0, n}], {n, 0, 14}]
A353042
G.f. A(x) satisfies: A(x) = 1 + x * A(4*x/(1 + 3*x)) / (1 - x).
Original entry on oeis.org
1, 1, 5, 73, 4301, 1065361, 1079026325, 4404504773593, 72088402948928861, 4722943066827454121761, 1237982543178169058402322725, 1298086594246614900499652230482793, 5444532149619463867564918804810528611821, 91343917667481554378430257939829428893551284401
Offset: 0
-
nmax = 13; A[] = 0; Do[A[x] = 1 + x A[4 x/(1 + 3 x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n - 1, k - 1] 2^(k (k - 1)), {k, 0, n}], {n, 0, 13}]
Showing 1-4 of 4 results.
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