A005642
Number of 2-diregular connected digraphs with n nodes.
Original entry on oeis.org
1, 3, 7, 24, 117, 663, 4824, 40367, 381554, 4001849, 46043780, 576018785, 7783281188, 112953364381, 1752128923245, 28930230194371, 506596534953769
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006372
Numbers of terms in expressions for coefficients of "Lovelock Lagrangians" (or "Gauss-Bonnet forms") in terms of Riemann-Christoffel curvature tensor and two of its contractions (viz., the Ricci curvature tensor and the Riemann curvature scalar) for n-dimensional differentiable manifolds having a general linear connection.
Original entry on oeis.org
1, 1, 3, 8, 25, 85, 397, 2183, 15129, 122585
Offset: 0
C. C. Briggs (ccb104(AT)vm.cac.psu.edu)
- C. Bogdanos, Diagrammatic derivation of Lovelock densities, Phys Rev. D 79 (10) (2009) 107501.
- C. C. Briggs, A General Expression for the Quintic Lovelock Tensor, arXiv:gr-qc/9607033, 1996-1997.
- C. C. Briggs, A General Expression for the Quartic Lovelock Tensor, arXiv:gr-qc/9703074, 1997.
- R. J. Mathar, 2-regular digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM], 2019.
A306827
Isomorphism classes of connected 2-in 2-out digraphs, allowing parallel edges but not loops.
Original entry on oeis.org
1, 2, 5, 13, 59, 285, 1987, 16057, 149430, 1551863, 17747299, 221015026
Offset: 2
For n=3, the a(3)=2 solutions consist of two superimposed directed triangles, one with the triangles oriented consistently and the other with the triangles oriented oppositely.
Cf.
A219889 (no multiedges, not necessarily connected),
A306892 (loops permitted),
A307180 (Euler transf.)
Showing 1-3 of 3 results.
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